12) Find the value of x. The image shows a circle with a center. Three points are on the circumference. Lines connect these points to form two triangles and two angles are given as 79 and 11 degrees. The angle x is indicated.

Analysis of the image

This problem is a geometry problem involving a circle and angles.

Problem 12 Analysis:

We have a circle with a center and points on the circumference. Lines form triangles, and given angles are 79° and 11°. We need to find the value of 'x'.

Solution Steps for Problem 12:

1. Let the vertices of the triangle on the circumference be A, B, and C. Let the angle at vertex A be x. Let the angle at vertex B be 79°. Let the angle at vertex C be 11°.
2. The sum of the angles in triangle ABC is 180°.
3. So, x + 79° + 11° = 180°.
4. Combine the known angles: 79° + 11° = 90°.
5. The equation becomes: x + 90° = 180°.
6. Solve for x: x = 180° - 90°.
7. x = 90°.

Final Answer for Problem 12: x = 90