Question

Angle ABC is inscribed in a circle as shown.

What is the measure, in degrees, of angle ABC?

Answer 1

Find out the measure, in degrees, of angle ABC .

To prove

The relationship between inscribed angles and their arcs

The measure of an inscribed angle is half the measure the intercepted arc.

The formula is

`Measure\ of\ inscribed\ angle = (1)/(2)* measure\ of\ intercepted\ arc`

As given in the diagram

The measure of the intercepted arc A to B is 120°.

Put value in the formula

`\angle ABC = (1* 120^(\circ))/(2)`

∠ABC = 60°

Therefore the measure of the ∠ABC is 60° .