Question

question 1 of 10 if chord $overline{ab}$ is congruent to chord $overline{bc}$, what is the measure of $angle boc$? a. $86^{circ}$ b. $43^{circ}$ c. $133^{circ}$ d. $47^{circ}$

Explanation:

Step1: Recall circle - chord property

In a circle, if two chords are congruent, then the central angles subtended by them are congruent.

Step2: Identify the relevant central angles

$\angle AOB$ and $\angle BOC$ are the central angles subtended by chords $\overline{AB}$ and $\overline{BC}$ respectively. Given $\overline{AB}\cong\overline{BC}$, so $\angle AOB=\angle BOC$.

Step3: Determine the measure of $\angle AOB$

From the figure, $\angle AOB = 43^{\circ}$.

Answer:

B. $43^{\circ}$