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y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

z = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

y = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.

x = °
💡 Key facts: right angle totals 90°, straight line totals 180°, full turn totals 360°.
Build the angle-sum first, e.g. “these angles make a straight line” means x + y = 180° or “around a point” means x + y + z = 360°.
Translate the sentence to algebra: “x is k times y” becomes x = k·y.
Comparatives help too: “x is a more than y” becomes x = y + a, and “x is a less than y” becomes x = y − a.
Substitute your algebra link into the angle-sum, combine like terms, then isolate the unknown with tidy inverse steps.
