### Example

In the figure below, angle *BAE* is an exterior angle of the circle with centre *O*.

### Property

The degree measure of angle *BAC* below is equal to one-half the difference of the degree measures of the arcs intercepted by the sides of the angle.

m\(\angle{\textrm{BAC}} = \frac{\textrm{m} \widehat{\textrm{DE}} – \textrm{m}\widehat{\textrm{BC}}}{2}\)

m\(\angle{\textrm{BAC}} = \frac{90 – 50}{2}=\frac{40}{2}=20\)