Question

Find the measure of each numbered angle or are.

Answer 1

<1 = 138degrees

<2 = 156degrees

Explanation:

From the diagram given;

angle at the vertex = 36degrees

Angle at the intercepted arc are <1 and 66degrees

Using the theorem;

Angle at the vertex is 1/2 the difference of the angles at the intercepted arcs

36 = 1/2(<1-66)

36*2 = <1-66

72 = <1 - 66

<1 = 72+66

<1 = 138degrees

Also since the sum of angle in a circle is 360degrees, hence;

<1 + <2 + 66 = 360

138 + <2 + 66 = 360

<2 + 204 = 360

<2 = 360 - 204

<2 = 156degrees