In the given figure, O is the center of the circle. Angle ABC = 100 degrees. Find the value of x.

Here's how we can solve this geometry problem step-by-step:

1. Understanding the relationship between angles: The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the remaining part of the circle. In this case, the arc AC subtends angle AOC at the center and angle ABC at the circumference.
2. Identifying the reflex angle: Since angle ABC is 100 degrees, it's an obtuse angle. This means the arc AC it subtends is the major arc. The angle AOC that subtends the minor arc AC is what we need to find first. The angle ABC (100 degrees) subtends the major arc AC.
3. Calculating the angle subtended by the major arc at the center: The angle subtended by the major arc AC at the center is equal to 2 * angle ABC. So, the reflex angle AOC = 2 * 100 degrees = 200 degrees.
4. Calculating the angle subtended by the minor arc at the center: The total angle around the center O is 360 degrees. Therefore, the angle AOC (the one that corresponds to x) is 360 degrees - 200 degrees = 160 degrees.
5. Relating to x: The angle x is the angle AOC, which subtends the minor arc AC.

Ответ: x = 160°