Question

Angle ABC is inscribed in a circle as shown.What is the measure, in degrees, of angle ABC?

Answer 1

Answer

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  

$Measure\ of\ inscribed\ angle = \frac{1}{2}\times measure\ of\ intercepted\ arc$

As given in the diagram

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

Put value in the formula

$\angle ABC = \frac{1\times 120^{\circ}}{2}$

∠ABC = 60°

Therefore the measure of the ∠ABC is 60° .