Question

A triangle has a bottom left angle of (x + 15) degrees and a bottom right angle of (x degrees). 1 parallel and horizontal line sits at the top point of the triangle. Another parallel and horizontal line sits at the base of the triangle. The exterior angle to the bottom right angle of the triangle is (4 x minus 20) degrees.
What is the value of x?

x = 32
x = 36
x = 37
x = 40

Answer 1

Use the exterior-angle theorem: an exterior angle equals the sum of the two remote interior angles.

Exterior at the bottom right = 4x − 20. The two remote interior angles are the bottom left (x + 15) and the top angle. Let the top angle be T. Then
4x − 20 = (x + 15) + T → T = 4x − 20 − (x + 15) = 3x − 35.

Sum of interior angles: (x + 15) + x + (3x − 35) = 180
5x − 20 = 180
5x = 200
x = 40

Answer: x = 40.