Question

solve for x: x° 52°

Explanation:

Step1: Recall tangent - radius property

A radius is perpendicular to the tangent at the point of tangency. The angle between the radius and the tangent is 90°.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle formed inside the circle, one angle is 90° (tangent - radius angle) and another is 52°. Let the third angle be \(x\). So, \(x + 90+52=180\).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180-(90 + 52)\\ x&=180 - 142\\ x&=38 \end{align*}$$

\]

Answer:

38