Question

line t is tangent to the circle. find ( moverset{\frown}{ab} )

Explanation:

Step1: Recall tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc.

Step2: Set up the equation

Let $m\overset{\frown}{AB} = x$. The given angle is $65^\circ$, so:
$65^\circ = \frac{1}{2}x$

Step3: Solve for $x$

Multiply both sides by 2:
$x = 65^\circ \times 2$

Answer:

$130^\circ$