Question

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

Answer 1

115

Explanation:

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Answer 2

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

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* x = 230^\circ\\\Rightarrow x = 115^\circ`

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