Question

question 10 of 10
if chord \\(\overline{ab}\\) is congruent to chord \\(\overline{bc}\\), what is the measure of \\(\angle boc\\)?

a. \\(47^\circ\\)

b. \\(133^\circ\\)

c. \\(86^\circ\\)

d. \\(43^\circ\\)

Explanation:

Step1: Recall chord-central angle rule

In a circle, congruent chords correspond to congruent central angles.

Step2: Identify given central angle

The central angle for chord $\overline{AB}$ is $\angle AOB = 43^\circ$.

Step3: Match congruent chords' angles

Since $\overline{AB} \cong \overline{BC}$, their central angles are equal: $\angle BOC = \angle AOB$.
<Expression>$\angle BOC = 43^\circ$</Expression>

Answer:

D. $43^\circ$