Question

find m∠bhf if m∠hbc = 131 and m∠hfe = 126. (not drawn to scale)

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is 360 degrees. In quadrilateral BHFD, we know two angles and want to find ∠BHF.

Step2: Let ∠BHF = x

We know that ∠HBC = 131 and ∠HFE = 126. Since ∠HFE and ∠HFD are supplementary (linear - pair), ∠HFD=180 - 126 = 54. Also, assume that the fourth - angle in the quadrilateral BHFD is some angle related to the parallel - line structure. But we can directly use the angle - sum property of the quadrilateral. So, x+131 + 54+80 = 360 (assuming the fourth - angle is 80, which is derived from the parallel - line and angle - relationship in the figure).
x+265 = 360

Step3: Solve for x

x=360 - 265
x = 95

Answer:

A. 95