Question

which of the following statements is true? answer attempt 1 out of 3
$m\angle ghj = 2(m\angle ihj)$ $m\angle ghj=\frac{1}{2}(m\angle ihj)$ $\frac{1}{2}(m\angle ghj)=m\angle ihj$ $m\angle ihj=\frac{1}{2}(m\angle ghi)$

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal parts. If $\overrightarrow{HJ}$ is the angle - bisector of $\angle GHI$, then $\angle GHJ=\angle IHJ$ and $\angle IHJ=\frac{1}{2}\angle GHI$.

Step2: Analyze each option

• Option 1: $\text{m}\angle GHJ = 2(\text{m}\angle IHJ)$ is incorrect as $\angle GHJ=\angle IHJ$ when $HJ$ is the angle - bisector.
• Option 2: $\text{m}\angle GHJ=\frac{1}{2}(\text{m}\angle IHJ)$ is incorrect since $\angle GHJ=\angle IHJ$.
• Option 3: $\frac{1}{2}(\text{m}\angle GHJ)=\text{m}\angle IHJ$ is incorrect as $\angle GHJ=\angle IHJ$.
• Option 4: Since $\overrightarrow{HJ}$ divides $\angle GHI$ into two equal angles $\angle GHJ$ and $\angle IHJ$, we have $\text{m}\angle IHJ=\frac{1}{2}(\text{m}\angle GHI)$. This is correct.

Answer:

$\text{m}\angle IHJ=\frac{1}{2}(\text{m}\angle GHI)$