Question

#31. I’m very confused. Solve?

Answer 1

Triangle ACD and Triangle CAB are the same or equivalent, and side AD is parallel to side BC. Find ∠B.

A triangle is 180°. To find x you can add all of the angles together and set it equal to 180°

37° + 3x° + (2x+8)° = 180°

Subtract 37° on both sides

3x° + (2x+8)° = 143°

3x° + 2x° + 8° = 143°

5x° = 135°

x = 27°

Since ∠D=∠B

3(27) = ∠B

81° = ∠B

Answer 2

Since the triangles are congruent, m<ACB = m<CAD = 2x + 8

m<B = m<D = 3x

m<CAB + m<B + m<ACB = 180

37 + 3x + 2x + 8 = 180

5x + 45 = 180

5x = 135

x = 27

m<CBA = m<B = 3x = 3(27) = 81

m<CBA = 81 deg