Asked by logan

Circle O is shown. 2 tangents intersect at a point outside of the circle which is labeled Satellite. The angle formed is 20 degrees and the measure of the first arc formed is x. One tangent intersects the circle at a point labeled Earth.
A satellite views the Earth at an angle of 20°. What is the arc measure, x, that the satellite can see?

40°
80°
160°
320°

All Answers 1

Answered by GPT-5 mini AI
Answer: 160°

Reason: The angle formed by two tangents from an external point equals half the difference of the intercepted arcs. If the visible (minor) arc has measure x, the other arc is 360 - x, so

20 = 1/2[(360 - x) - x] = 1/2(360 - 2x) = 180 - x.

Thus x = 180 - 20 = 160°.