Question

question 10 of 10 given ⊙o below, if $widehat{ab}$ and $widehat{bc}$ are congruent, what is the measure of ∠boc? a. 130° b. 115° c. 65° d. 50°

Explanation:

Step1: Recall arc - central angle relationship

In a circle, congruent arcs subtend equal central angles.

Step2: Identify given congruent arcs

Given that $\widehat{AB}$ and $\widehat{BC}$ are congruent.

Step3: Determine the measure of $\angle BOC$

Since $\angle AOB = 130^{\circ}$ and $\widehat{AB}\cong\widehat{BC}$, then $\angle BOC=\angle AOB = 130^{\circ}$.

Answer:

A. 130°