Equilateral triangle pbj is inscribed in a circle as shown. determine the measure of arc pb

The measure of arc PB is 120°

Step-by-step explanation:

Given: A equilateral triangle PBJ is inscribed in a circle with centre O as shown in attachment.

PBJ is an equilateral triangle. Equilateral triangle has equal angles and sides.

Measure of each angle equilateral triangle is 60°

Hence, ∠BJP=60°

∠BOP and ∠BJP lie on same arc of circle but ∠BJP make at circumference of circle and ∠BOP make at centre of circle.

∠BOP=2∠BJP (Because the angle which is subtended by an arc at the centre of a circle is double the size of the angle subtended at any point on the circumference)

Thus, ∠BOP=2 x 60 = 120°

Hence, The measure of arc PB is 120°