Question

Given o below, if ab and BC are congruent, what is the measure of BOC? 130

Answer 1

Answer:

$B.\ 115^\circ$ is the correct answer.

Step-by-step explanation:

It is given that $O$  is the center of the circle and $\angle AOC = 130 ^\circ$.

Also it is given that arc $\frown{AB} \text{ and } \frown BC$ are congruent that means they make equal angles at the center $O$. Let the angle be $x ^\circ$.

Also, we know that the total angle made at the center of the circle is $360^\circ$.

The given circle of question figure is divided in 3 arcs, so sum of angles made by all of them at the center is $360^\circ$.

$\Rightarrow 130 ^\circ + x +x=360^\circ\\\Rightarrow 2\times x = 230^\circ\\\Rightarrow x = 115^\circ$

Hence $B.\ 115^\circ$ is the correct answer for this question.