Question

In the diagram, g ∥ h, m∠1 = (4x + 36)°, and
m∠2 = (3x – 3)°.

Lines g and h are parallel and diagonal down to the right. A horizontal line cuts through lines g and h. Another vertical line goes through lines g and h and the horizontal line. At the intersection of the vertical line with line h, the bottom left angle is angle 1 and the bottom right angle is angle 3. At the intersection of the vertical line with line g, the uppercase left angle is angle 2.

What is the measure of ∠3?

21°
60°
120°
159°

Answer 1

Because g ∥ h and the vertical line is a transversal, ∠1 and ∠2 are same-side interior angles, so they are supplementary:

(4x + 36) + (3x − 3) = 180
7x + 33 = 180
7x = 147
x = 21

Then ∠1 = 4(21) + 36 = 120°. ∠3 is the adjacent angle (linear pair) to ∠1, so
∠3 = 180° − 120° = 60°.

Answer: 60°.