Question

hk bisects ∠ghj. find m∠ghk and m∠khj. angle jhg measures 161. m∠ghk=80.5, m∠khj=161; m∠ghk=161, m∠khj=80.5; m∠ghk=80.5, m∠khj=80.5; m∠ghk=161, m∠khj=161

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal parts.

Step2: Identify the given angle

We are given that $\angle JHG = 161^{\circ}$ and $\overrightarrow{HK}$ bisects $\angle GHJ$.

Step3: Calculate the measure of sub - angles

If $\overrightarrow{HK}$ bisects $\angle GHJ$, then $m\angle GHK=m\angle KHJ=\frac{1}{2}m\angle GHJ$. So $m\angle GHK = m\angle KHJ=\frac{161}{2}=80.5^{\circ}$.

Answer:

C. $m\angle GHK = 80.5$, $m\angle KHJ=80.5$