First, find the surface area of the yellow prism

Check the picture below.  Notice, we're skipping the bottom part of it.

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°.