We are given a circle with center at a point (let's call it O). We have three points on the circumference: R, S, and T. We are given that the segments OR and OT are radii of the circle, so they have equal length. This makes triangle ORT an isosceles triangle. We are given that angle RT measures 58 degrees, and we need to find the value of angle R, which is labeled as $x$ degrees.

1. Problem Description

We are given a circle with center at a point (let's call it O). We have three points on the circumference: R, S, and T. We are given that the segments OR and OT are radii of the circle, so they have equal length. This makes triangle ORT an isosceles triangle. We are given that angle RT measures 58 degrees, and we need to find the value of angle R, which is labeled as $x$ degrees.

2. Solution Steps

Since triangle ORT is isosceles with OR = OT, then the base angles at R and T are equal. Therefore, angle R = angle T. We are given that angle T = 58 degrees, so angle R = 58 degrees. Since angle R is labeled as $x$ degrees, we have $x = 58$.

However, we are looking for the measure of the *angle* at the vertex S, not angle R. The sum of the angles in any triangle is 180 degrees. So in triangle RST, angle R + angle T + angle S = 180 degrees.

Therefore, angle S = 180 degrees - angle R - angle T. So, angle S = 180 - 58 - 58 = 180 - 116 = 64 degrees. Since angle S is labeled as $x$ degrees, we have $x = 64$.

3. Final Answer

64