Question

which of the following statements is true? answer m∠nop = m∠noq 2(m∠noq) = m∠nop 2(m∠noq) = m∠poq m∠nop = m∠poq

Explanation:

Step1: Observe the angle - relationship

From the figure, ray $OQ$ is between $\angle NOP$. So, $\angle NOP=\angle NOQ + \angle QOP$.

Step2: Analyze the options

If $OQ$ is the angle - bisector of $\angle NOP$, then $\angle NOQ=\angle QOP$ and $\angle NOP = 2\angle NOQ$. But we are not given that $OQ$ is the angle - bisector. However, we know that $\angle NOP$ is composed of $\angle NOQ$ and $\angle QOP$. So, the correct relationship is $2(\angle NOQ)=\angle NOP$ when $OQ$ is the angle - bisector. In general, we can see from the figure that $\angle NOP$ is larger than $\angle NOQ$ and if we assume $OQ$ bisects $\angle NOP$, we have the double - angle relationship.

Answer:

$2(m\angle NOQ)=m\angle NOP$