Question

Two angles lie along a straight line. If m∠A
is five times the sum of m∠B
plus 7.2°, how many degrees is m∠B?


A horizontal line has a ray that extends up and right. The angle formed on the left of the ray is labelled A and the angle formed on the right of the ray is labelled B.

Answer 1

Angles on a straight line are supplementary, so m∠A + m∠B = 180°.

Given m∠A = 5(m∠B + 7.2°), substitute:
5(mB + 7.2) + mB = 180
5mB + 36 + mB = 180
6mB = 144
mB = 24°

Check: mA = 5(24 + 7.2) = 5(31.2) = 156°, and 156° + 24° = 180°. So m∠B = 24°.