Question

given:

• (overrightarrow{iq}) bisects (angle xir).
• (mangle xir = 120^{circ}).

enter each measure required to calculate (mangle qij), starting with the given information.
the measure of (angle quj) can be calculated.
(mangle quj = 120^{circ})
the measure of (angle qij) can not be calculated.
diagram notes:
enter the given angle measure into the diagram.
the measure of (angle qir) can be calculated
(mangle qir=)

Explanation:

Step1: Recall the angle - bisector definition

Since \( \overrightarrow{IQ}\) bisects \( \angle XIR\), by the definition of an angle bisector, if \(m\angle XIR = 120^{\circ}\), then \(m\angle QIR=\frac{1}{2}m\angle XIR\).

Step2: Calculate \(m\angle QIR\)

Substitute \(m\angle XIR = 120^{\circ}\) into the formula \(m\angle QIR=\frac{1}{2}m\angle XIR\). So \(m\angle QIR=\frac{1}{2}\times120^{\circ}\).

Answer:

\(60^{\circ}\)