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📘 Math Olympiad Question – Geometry Angle Problem

Question:
If line m ∥ n, then find the value of x in the figure below


Math Olympiad Geometry Problem with parallel lines solution :

🔎 Step-by-Step Solution

  1. From the figure:
    - Left base angle = 2y
    - Right base angle = 84°
    - Outside angle at top = 3y
    - Inside angle at top = x

  2. Given: 3y = 84°
    ⇒ y = 84 ÷ 3 = 28°

  3. Now, left base angle = 2y = 56°

  4. Using triangle angle sum property:
    x + 56° + 84° = 180°
    x + 140° = 180°
    x = 40°

✅ Final Answer

x = 40°

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