In the triangle, opposite the diameter is 180°. Smaller angles sum to 180°, so x = 180 - 58 = 122° and the correct option is 1.
The diagram shows a circle with a triangle inside it. The triangle has two sides that are tangent to the circle, and the third side is the diameter of the circle. The angle measure of one of the smaller angles of the triangle is given as 58 degrees. We are asked to find the measure of the angle marked x.
To find the measure of angle x, we can use the fact that the sum of the angles in a triangle is 180 degrees. We can also use the fact that the angles formed by a tangent and a radius at the point of tangency are right angles.
Here are the steps to solve for x:
1. Identify the right angles: Since the two sides of the triangle are tangent to the circle, the angles where they meet the circle are right angles.
2. Find the angle measures of the two smaller angles: The angle measure of one of the smaller angles is given as 58 degrees. The other smaller angle is opposite the diameter of the circle, which is a straight line and therefore has an angle measure of 180 degrees. Since the two smaller angles are supplementary, their sum is 180 degrees. Therefore, the measure of the other smaller angle is 180 degrees - 58 degrees = 122 degrees.
3. Find the measure of angle x: The measure of angle x is equal to the sum of the measures of the two smaller angles in the triangle. Therefore, the measure of angle x is 122 degrees + 58 degrees = 180 degrees.
Therefore, the answer is 122° and the correct option is 1.