Answer:
<1 = 138degrees
<2 = 156degrees
Step-by-step 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
