what is the measure of angle ABC?

Question

The circle shown below has AB and BC as its tangents:

If the measure of arc AC is 160°, what is the measure of angle ABC? (1 point)

		80°
		40°
		60°
		20°

Answer 1

Hello,

The questions tells you that these are two tangent lines. By definition of intersections outside of a circle, when there are 2 tangent lines the angle measure is 1/2 the difference between the intercepted arcs. Therefore, given the arc angle of AC of 160, the other arc angle is 200. This is found because a circle is 360 degrees total and subtracting 160 from 360 equals 200. Then the difference between 200 and 160 is 40 and half of 40 is 20. Therefore, the correct answer is 20 degrees.