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 formula for the measure of an angle formed by two tangents

The measure of an angle formed by two tangents drawn from an external point to a circle is given by \( \theta=\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})\). Let \(m\overset{\frown}{minor} = x\) and \(m\overset{\frown}{major}=360 - x\). The angle \(\theta = 20^{\circ}\).

Step2: Substitute into the formula

We know that \(20=\frac{1}{2}((360 - x)-x)\).
First, simplify the right - hand side: \(20=\frac{1}{2}(360 - 2x)\).
Multiply both sides by 2: \(40=360 - 2x\).
Then, add \(2x\) to both sides: \(2x + 40=360\).
Subtract 40 from both sides: \(2x=360 - 40=320\).
Divide both sides by 2: \(x = 160^{\circ}\).

Answer:

\(160^{\circ}\)