Question

in the diagram below, $overline{ad}paralleloverline{eg}$, $overline{bh}perpoverline{fc}$, and $mangle abh = 149^{circ}$. find $mangle efh$. you may assume lines that appear straight are straight but the figure is not otherwise drawn to scale. answer attempt 2 out of 6 $mangle efh=$

Explanation:

Step1: Find m∠HBC

Since ∠ABH + ∠HBC = 180° (linear - pair of angles), and m∠ABH = 149°, then m∠HBC=180° - 149° = 31°.

Step2: Use parallel - line property

Because $\overline{AD}\parallel\overline{EG}$, and $\overline{BH}\perp\overline{FC}$, ∠EFH and ∠HBC are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are congruent. So m∠EFH = m∠HBC.

Answer:

31°