Question

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°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. Let the central angle corresponding to arc $x$ be $\theta$. The angle at the satellite is an inscribed - like angle. If the angle at the satellite is $20^{\circ}$, and the central angle $\theta$ and the angle at the satellite are related by the formula for angles formed by tangents and secants from an external point. The central angle $\theta$ is twice the angle at the satellite.

Step2: Calculate the arc measure

We know that the measure of the arc $x$ is equal to the measure of the central angle that intercepts it. Since the angle at the satellite is $20^{\circ}$, the central angle corresponding to arc $x$ is $40^{\circ}$ (because the angle formed by two tangents from an external point to a circle is half the difference of the intercepted arcs, and in this case, the relevant relationship is that the central angle is twice the angle at the external point). So $x = 40^{\circ}$.

Answer:

$40^{\circ}$