Question

in the diagram below, m∠cih = 107° and m∠bgd = 39°. find m∠fhg. you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale. answer attempt 2 out of 2 m∠fhg =

Explanation:

Step1: Identify vertical - angles

$\angle CIH$ and $\angle EIG$ are vertical - angles. So, $m\angle EIG=m\angle CIH = 107^{\circ}$.

Step2: Use the exterior - angle property of a triangle

In $\triangle EHG$, $\angle EIG$ is an exterior angle. According to the exterior - angle property of a triangle, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. Here, $\angle EIG=\angle EHG+\angle HGE$. We know that $\angle HGE = \angle BGD=39^{\circ}$ (vertical angles) and $\angle EHG=\angle FHG$. Let $x = m\angle FHG$. Then $107^{\circ}=x + 39^{\circ}$.

Step3: Solve for $\angle FHG$

Subtract $39^{\circ}$ from both sides of the equation $107^{\circ}=x + 39^{\circ}$. So, $x=m\angle FHG=107^{\circ}-39^{\circ}=68^{\circ}$.

Answer:

$68$