From the image, what is the value of angle BOC?

In the first diagram, we are given that angle BAC = 36 degrees. This inscribed angle subtends arc BC. The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, the measure of arc BC is 2 * angle BAC = 2 * 36 degrees = 72 degrees.

The central angle that subtends the same arc BC is angle BOC. The measure of a central angle is equal to the measure of its intercepted arc.

Therefore, angle BOC = measure of arc BC = 72 degrees.

Ответ: 72°