Question

If ∠1 ≅ ∠2 ≅ ∠3, ∠4 ≅ ∠5, and m∠4 = m∠3 + 10, What is m∠5?

Six lines and rays intersect to form a 6 sided figure with vertices at 1, 2, 3, 4, 5, and 6. Angle 6 is a right angle.

Answer 1

m∠5 = 132°.

Reason: Let m∠1 = m∠2 = m∠3 = x and m∠4 = m∠5 = y, with y = x + 10 and m∠6 = 90°. The sum of interior angles of a hexagon is 720°, so
3x + 2y + 90 = 720.
Substitute y = x + 10: 3x + 2(x + 10) + 90 = 720 → 5x + 110 = 720 → x = 122°.
Then y = x + 10 = 132°, so m∠5 = 132°.