Res 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°

The arc measure, x, that the satellite can see is 160°

Step-by-step explanation:

Given that the two tangents intersect at a point outside the with circle center O

The angle formed between between the two tangent = 20°

The first arc formed is measured as x°, which is the arc opposite the point where the two tangents meet = The arc the satellite can see

The angle x is given by the relationship;

x = 2 × (90 - v/2)

Where;

v = The angle formed at the point where the two tangent meet = 20°

Therefore;

x = 2 × (90 - 20/2) =  2 × (90 - 10) =  2 × 80  = 160°

The arc measure, x, that the satellite can see = 160°.