Question

A tangent and a secant x = ?

Answer 1

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.

$\Rightarrow x = \frac{1}{2}(\text{ larger arc }- \text{smaller arc} )$

$\Rightarrow x = \frac{1}{2}(152^\circ-62^\circ)$

$\Rightarrow x = \frac{1}{2}(90^\circ)$

⇒ x = 45°

The value of x is 45°.