Question

The measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x – 15)°.

Vertical and parallel lines c, d, and e are cut by diagonal transversal a. On line c where it intersects with line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line b where it intersects with line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5.
What is the measure of angle 7?

°

Answer 1

Angle 1 and angle 4 are vertical angles, so they are equal:
3x + 10 = 4x − 15
Solve: 25 = x, so angle 1 = 3(25) + 10 = 85°.

Angle 3 is the linear pair with angle 1, so angle 3 = 180° − 85° = 95°.

Angle 7 is corresponding to angle 3 (same position on the other parallel line), so angle 7 = 95°.