Question

given:
og bisects ∠cox.

• m∠jog = 120°.

enter the measures and reasons to justify each needed to calculate m∠cox.
m∠cox =
diagram notes:
first, enter the given information for ∠jog.
m∠jog = 120°

Explanation:

Step1: Find the measure of ∠COG

Since \(m\angle JOG = 120^{\circ}\) and \(\angle JOG\) and \(\angle COG\) are supplementary (they form a linear - pair), we use the formula \(m\angle COG=180^{\circ}-m\angle JOG\).
\(m\angle COG = 180^{\circ}- 120^{\circ}=60^{\circ}\)

Step2: Use the angle - bisector property

Given that \(\overline{OG}\) bisects \(\angle COX\), by the definition of an angle bisector (\(m\angle COG=m\angle GOX\)).
Since \(m\angle COG = 60^{\circ}\), then \(m\angle GOX=60^{\circ}\)

Step3: Calculate \(m\angle COX\)

By the angle - addition postulate (\(m\angle COX=m\angle COG + m\angle GOX\))
\(m\angle COX=60^{\circ}+60^{\circ}\)

Answer:

\(120\)