Question

Quick answer, please. This would really help me out.

Answer 1

Given:

Circle with chord and tangent.

To find:

The measure of angle 1.

Solution:

Let 2 be the adjacent angle of angle 1.

If a tangent and a chord intersect at a point, then the angle formed is half of the measure of the intercepted arc.

`$\Rightarrow m\angle 2=(1)/(2) (248)^\circ`

`$\Rightarrow m\angle 2=124^\circ`

Sum of the adjacent angles in a straight line is 180°.

⇒ m∠1 + m∠2 = 180°

⇒ m∠1 + 124° = 180°

Subtract 124° from both sides.

⇒ m∠1 = 56°

The measure of angle 1 is 56°.