Question

in the diagram below, m∠cih = 103° and m∠bgd = 37°. find m∠ihg. 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∠ihg =

Explanation:

Step1: Identify vertical - angle

$\angle CIH$ and $\angle EIG$ are vertical angles. Since vertical angles are equal, $m\angle EIG = m\angle CIH=103^{\circ}$.

Step2: Use the exterior - angle property

In $\triangle IHG$, $\angle EIG$ is an exterior angle. The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let $m\angle IHG=x$ and $m\angle HGI = m\angle BGD = 37^{\circ}$ (vertical angles).
By the exterior - angle property of a triangle, $m\angle EIG=m\angle IHG + m\angle HGI$.
We know $m\angle EIG = 103^{\circ}$ and $m\angle HGI=37^{\circ}$, so $103^{\circ}=x + 37^{\circ}$.

Step3: Solve for $m\angle IHG$

Subtract $37^{\circ}$ from both sides of the equation $103^{\circ}=x + 37^{\circ}$.
$x=m\angle IHG=103^{\circ}-37^{\circ}=66^{\circ}$.

Answer:

$66$