Question

line t is tangent to the circle. find mab
mab = □°

Explanation:

Step1: Use the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the measure of the intercepted arc. Let \(m\overset{\frown}{AB}=x\). The formula is \(\text{Angle}=\frac{1}{2}\text{Intercepted arc}\).
The angle between the tangent \(t\) and the secant \(AB\) is \(65^{\circ}\).

Step2: Solve for the arc measure

We know that \(65^{\circ}=\frac{1}{2}m\overset{\frown}{AB}\).
Multiply both sides of the equation by \(2\): \(m\overset{\frown}{AB}=2\times65^{\circ}\).

Answer:

\(130\)