Question

m∠6 is (2x – 5)° and m∠8 is (x + 5)°.

Parallel lines q and s are cut by transversal r. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line s where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7.
What is m∠3?

°

Answer 1

Angles 6 and 8 are a linear pair, so (2x − 5) + (x + 5) = 180.
3x = 180 → x = 60.
m∠6 = 2(60) − 5 = 115°.

∠3 and ∠6 are alternate interior angles (lines q and s are parallel), so m∠3 = m∠6 = 115°.