Type the correct answer in each box.

Question

Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circle.

Given  and , ____° and  ____°.

Answer 1

ABC forms a triangle.

m<ACB = 1/2 measure of intercepted arc AB (64) = 32.

sum of angles of triangle ABC = 180, since m<ACB = 32 and m<ABC = 73, then m<CAB = 180 - 73 - 32 = 75.

since m<CAB = 75, the measure of the intercepted arc BC = 150.

measure of arc ABC = measure of arc AB + arc BC = 64 + 150 = 214.

The measure of the entire circle is 360. So the measure of the arc AC would be 360-214 = 146.