Question

the angle bisector of \\( \angle npm \\) is \\( \overrightarrow{pq} \\). write an equation to describe the relationship between \\( m \angle npm \\) and \\( m \angle qpm \\).
choose the correct answer below.
a. \\( m \angle npm = 2 ( m \angle qpm ) \\)
b. \\( m \angle npm = m \angle qpm \\)
c. \\( m \angle npm = \frac { 1 } { 2 } ( m \angle qpm ) \\)
d. \\( m \angle npm = 3 ( m \angle qpm ) \\)

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal - sized angles.
Since \(\overrightarrow{PQ}\) is the angle bisector of \(\angle NPM\), then \(\angle NPQ=\angle QPM\) and \(\angle NPM=\angle NPQ + \angle QPM\).

Step2: Substitute \(\angle NPQ\) with \(\angle QPM\)

Substituting \(\angle NPQ\) with \(\angle QPM\) in the equation \(\angle NPM=\angle NPQ+\angle QPM\), we get \(m\angle NPM=m\angle QPM + m\angle QPM\).

Step3: Simplify the equation

Simplifying \(m\angle NPM=m\angle QPM + m\angle QPM\) gives \(m\angle NPM = 2(m\angle QPM)\).

Answer:

A. \(m\angle NPM = 2(m\angle QPM)\)