Question

the angle bisector of \\( \angle pqr \\) is \\( \overrightarrow{qe} \\). if \\( m \angle pqe = 2n^{\circ} \\), what is \\( m \angle pqr \\)?
a \\( n^{\circ} \\)
b \\( 2n^{\circ} \\)
c \\( 4n^{\circ} \\)

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal parts. So, \(m\angle PQE=m\angle EQ R\).

Step2: Calculate \(m\angle PQR\)

Since \(m\angle PQR = m\angle PQE+m\angle EQ R\) and \(m\angle PQE = m\angle EQ R=2n^{\circ}\), then \(m\angle PQR=2n^{\circ}+2n^{\circ}\).

$$m\angle PQR = 4n^{\circ}$$

Answer:

C. \(4n^{\circ}\)