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.
[tex]$\Rightarrow m\angle 2=\frac{1}{2} (248)^\circ[/tex]
[tex]$\Rightarrow m\angle 2=124^\circ[/tex]
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°.
