# Inscribed Angle

## Inscribed Angle

An angle whose vertex is on a circle and whose sides are chords of the circle.

### Property

The degree measure of an inscribed angle is equal to one-half of the degree measure of the arc intercepted by the sides of the angle.

### Example

• In the figure below, angle BAC is an angle inscribed in the circle with centre O.

• $$m∠\textrm{BAC} = \frac{\textrm{m} {\widehat{\textrm{BC}}}}{2}$$

$$m∠\textrm{BAC} = \frac{60}{2}= 30$$

• The degree measure of an angle inscribed in a semicircle is equal to that of a right angle.