Question

given that m∠qpr = 43.5° and pq is the angle bisector of ∠npr. select the three statements that are true. note: figure may not be to scale a m∠npq = 43.5° b m∠npq = m∠rpq c m∠npq + m∠qpr = 43.5° d m∠npr = 43.5° e m∠rpn = 87°

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. Since $\overrightarrow{PQ}$ is the angle - bisector of $\angle NPR$, then $\angle NPQ=\angle QPR$.

Step2: Calculate $\angle NPR$

Given $\angle QPR = 43.5^{\circ}$, and $\angle NPQ=\angle QPR$, so $\angle NPR=\angle NPQ+\angle QPR=43.5^{\circ}+43.5^{\circ}=87^{\circ}$.

Answer:

A. $m\angle NPQ = 43.5^{\circ}$
B. $m\angle NPQ=m\angle RPQ$
E. $m\angle RPN = 87^{\circ}$