Question

Equilateral triangle PBJ is inscribed in a circle as shown. Determine the measure of arc PB.

Answer 1

The measure of arc PB is 120°.

Explanation:

Since the diagram is missing,we have attached the diagram for your reference.

Given,

ΔPBJ is an equilateral triangle.

We have to find the measure of arc PB.

Solution,

Since ΔPBJ is an equilateral triangle.

And we know that each angle of an equilateral triangle is equal to 60°.

`\angle BJP=60\°`

Now according to inscribed angle theorem, which states that;

"The angle subtended by an arc at the center is double the angle subtended by it at any remaining part of the circle".

so we can say that;

`m\ of\ arc\ PB=2*\angle BJP`

On substituting the value, we get;

`m\ of\ arc\ PB=2*60\°=120\°`

Hence The measure of arc PB is 120°.