Question

question 1 of 10 given ⊙o below, if $widehat{gh}$ and $widehat{hj}$ are congruent, what is the measure of ∠goh? a. 300° b. 150° c. 120° d. 60°

Explanation:

Step1: Recall circle - arc relationship

In a circle, if two arcs are congruent, the central angles that intercept them are congruent.

Step2: Identify given congruent arcs

We are given that $\widehat{GH}$ and $\widehat{HJ}$ are congruent. Let $\angle GOH$ be the central - angle for $\widehat{GH}$ and $\angle HOJ$ be the central - angle for $\widehat{HJ}$.

Step3: Observe the known angle

We see that $\angle HOJ = 60^{\circ}$.

Step4: Determine $\angle GOH$

Since $\widehat{GH}\cong\widehat{HJ}$, then $\angle GOH=\angle HOJ = 60^{\circ}$.

Answer:

D. 60°