Question

line m is tangent to the circle. find the measure of ∠1.
210°
m∠1=□°

Explanation:

Step1: Find the measure of the intercepted arc

The measure of the arc that is not \(210^{\circ}\) is \(360^{\circ}-210^{\circ}=150^{\circ}\)

Step2: Use the tangent - secant angle formula

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
If \(\angle1\) is formed by a tangent \(m\) and a chord, and the intercepted arc has measure \(x = 150^{\circ}\), then \(m\angle1=\frac{1}{2}x\)
Substitute \(x = 150^{\circ}\) into the formula: \(m\angle1=\frac{1}{2}\times150^{\circ}=75^{\circ}\)

Answer:

\(75\)