Question

line t is tangent to the circle. find m∠1

m∠1 = □°.

Explanation:

Step1: Find the minor arc measure

The total degrees in a circle is $360^\circ$. Subtract the given major arc:
$360^\circ - 260^\circ = 100^\circ$

Step2: Calculate $\angle 1$ measure

The angle formed by a tangent and chord is half its intercepted arc:
$m\angle 1 = \frac{1}{2} \times 100^\circ$

Answer:

$50$