Question

in the diagram, ∠jkm is a straight angle. which statements about the diagram are true? choose three correct answers. kq→ is an angle bisector. ∠jkl≅∠qkm m∠jkl = 45° m∠mkq + m∠pkq = m∠pkm

Explanation:

Step1: Analyze angle - bisector condition

No info shows $\overrightarrow{KQ}$ bisects an angle.

Step2: Check vertical - angle property

$\angle{JKL}$ and $\angle{QKM}$ are vertical angles, so $\angle{JKL}\cong\angle{QKM}$.

Step3: Analyze angle measure

No info gives $m\angle{JKL}=45^{\circ}$.

Step4: Use angle - addition postulate

By angle - addition postulate, $m\angle{MKQ}+m\angle{PKQ}=m\angle{PKM}$.

Answer:

$\angle{JKL}\cong\angle{QKM}$, $m\angle{MKQ}+m\angle{PKQ}=m\angle{PKM}$