Question

find the indicated angle measure. a. 52° b. 64° c. 256° d. 38°

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. Let's consider the circle - related angle properties. The central angle is \(128^{\circ}\). The angle formed by the two radii and the two tangents has a relationship with the central angle.

Step2: Use the formula for the angle between two tangents

The measure of the angle \(x\) between two tangents to a circle is given by \(x = \frac{1}{2}(360^{\circ}-\text{central angle})\). Here, the central angle is \(128^{\circ}\). First, find \(360 - 128=232^{\circ}\). Then, \(x=\frac{1}{2}\times232^{\circ}= 52^{\circ}\).

Answer:

A. \(52^{\circ}\)