Question

enter the given angle measure into the diagram.
given:

• (overline{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 qij) can be calculated.

(mangle qij = 120^{circ})

• the measure of (angle qij) can not be calculated.

diagram notes:

Explanation:

Step1: Use the angle - bisector property

Since \( \overline{IQ}\) bisects \( \angle XIR\), then \(m\angle QIX=\frac{1}{2}m\angle XIR\). Given \(m\angle XIR = 120^{\circ}\), so \(m\angle QIX=\frac{1}{2}\times120^{\circ}=60^{\circ}\).

Step2: Use the linear - pair (or straight - angle) property

We know that \(m\angle JIX = 180^{\circ}\) (a straight - angle). Also, \(m\angle JIX=m\angle JIR + m\angle RIQ+m\angle QIX\). But if we consider \(m\angle JIU\), we know that \(m\angle JIU + m\angle QIX=180^{\circ}\) (linear - pair of angles).
Substitute \(m\angle QIX = 60^{\circ}\) into the equation \(m\angle JIU=180^{\circ}-m\angle QIX\).

Answer:

\(m\angle JIU = 120^{\circ}\)