x = 45°
Solution:
Given data:
Measure of larger arc = 152°
Measure of smaller arc = 62°
If a tangent and a secant intersect at the exterior of a circle then the measure of angle formed is one-half the positive difference of the measures of the intercepted arcs.
[tex]$\Rightarrow x = \frac{1}{2}(\text{ larger arc }- \text{smaller arc} )[/tex]
[tex]$\Rightarrow x = \frac{1}{2}(152^\circ-62^\circ)[/tex]
[tex]$\Rightarrow x = \frac{1}{2}(90^\circ)[/tex]
⇒ x = 45°
The value of x is 45°.
