Question

ig bisects ∠cij.
m∠cix = 150°.
enter the measures and reasons to justify each s
needed to calculate m∠gir.
m∠gir=
diagram notes:
first, enter the given information for ∠cix.
m∠cix = 150°
next, calculate the m∠jix.
m∠jix = 90°

Explanation:

Step1: Analyze the straight - angle

A straight - angle measures \(180^{\circ}\). Since \(\angle CIX = 150^{\circ}\), and \(\angle CIX+\angle XIR = 180^{\circ}\) (they form a linear pair), then \(\angle XIR=180 - 150=30^{\circ}\).

Step2: Use the angle - bisector property

Given that \(IG\) bisects \(\angle CIJ\). Let's first find \(\angle CIJ\). \(\angle CIJ = 180^{\circ}-\angle JIX\) (assuming \(X\) is on a straight line with \(C\) and \(J\) in the relevant angle - formation context). But from the diagram, we can also note that \(\angle GIR=\angle GIC+\angle CIR\). Since \(IG\) bisects \(\angle CIJ\) (not fully necessary for this simple sum from the diagram's given angles), and directly from the angle measures in the diagram (by adding the non - overlapping adjacent angles that make up \(\angle GIR\)): \(\angle GIR = 60^{\circ}\) (by adding the \(30^{\circ}\) and \(30^{\circ}\) adjacent angles to the \(60^{\circ}\) - labeled angle in the correct combination as per the angle composition at point \(I\)).

Answer:

\(60\)