Question

Two parallel lines are cut by a transversal as shown below.
Suppose m1=64°. Find m6 and m 8.

Answer 1

∠ 6 = 116° , ∠ 8 = 116°

Explanation:

∠ 3 and ∠ 1 are vertically opposite angles and are congruent , then

∠ 3 = ∠ 1 = 64°

∠ 3 and ∠ 6 are same side interior angles and sum to 180° , that is

∠ 3 + ∠ 6 = 180°

64° + ∠ 6 = 180° ( subtract 64° from both sides )

∠ 6 = 116°

∠ 6 and ∠ 8 are vertically opposite angles and are congruent , then

∠ 8 = 116°