Question

A bike path crosses a road as shown. Solve for each indicated angle measure or variable.

Answer 1

Given:
84° angle
4x angle
angle M  

The angle that measures 84° and the angle that measures 4x are vertical angles. This means that their angle measures are congruent. Thus, the value of x is 21°

84° = 4x
84° / 4 = x
21° = x

Angle M and the angle that measures 84° are supplementary angles. This means that the sum of their measure equals 180°. Thus, angle M measures 96°.

84° + M = 180°
M = 180° - 84°
M = 96°