Question

11. You are asked to put a V-shaped roof on a house. The slope of the roof is 53°. What is the measure of the angle needed at the vertex of the roof? (Hint: You are given the base angles, and you need to find the vertex angle.)

Answer 1

X=missing angle

53(2)+x=180

106+x=180

180-106= 74

The vertex angle is 74. 

Answer 2

The question said that it told you the base angles. A roof would have two equal base angles. The base angles= 53

All the angles of a triangle each 180, (the roof is shaped like a triangle)

So, let's make x the missing angle.

53(2)+x=180

106+x=180

Subtract 106 on both sides.

180-106= 74

The vertex angle is 74.

I hope this helps!
~cupcake