Question

in the diagram below, ad || eg, bh ⊥ fc, and m∠abh = 145°. find m∠efh. you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale. answer attempt 1 out of 2 m∠efh = □°

Explanation:

Step1: Find m∠HBC

Since ∠ABH and ∠HBC are supplementary (a straight - line angle is 180°), and m∠ABH = 145°, then m∠HBC=180° - 145° = 35°.

Step2: Use properties of right - triangle

In right - triangle BCH, ∠BHC = 90° (because BH⊥FC). In triangle BCH, we know that the sum of the interior angles of a triangle is 180°. Let's consider the relationship between the angles in the figure. Since AD∥EG, ∠EFC and ∠BCF are corresponding angles. Also, in right - triangle BCH, we find the angle related to ∠EFH.
We know that ∠HBC + ∠BCH=90° (in right - triangle BCH). So, ∠BCH = 90° - 35° = 55°.
Because AD∥EG, ∠EFH=∠BCH (corresponding angles).

Answer:

55