Question

Please help meeee! A new crosswalk is being built between the parallel sidewalks of Circle Avenue. The edges of the crosswalk are parallel. One angle that the crosswalk makes with the sidewalk measures 78 degrees, as shown. Determine the measures of the missing angles. The drawing is not drawn to scale.

Answer 1

`A = 78^\circ`

`B = 102^\circ`

`C = 102^\circ`

Explanation:

Given

The attached image

Required

Find A, B and C

Because the sides of the crosswalk are parallel and the sidewalks are also parallel, then the following relationships exist

`A = 78^\circ` ---- alternate interior angles

`B = C` ---- alternate interior angles

To solve for B, we have:

`B + 78 = 180` --- the sum of the base angles

`B = 180 - 78`

`B = 102^\circ`

Recall that:

`B = C`

`C = 102^\circ`