6. In the figure, point O is the center of the circle. The angle OBA = 76 degrees. Find the angle AOB.

This problem involves a circle with center O and a triangle AOB where OA and OB are radii. We are given that angle OBA = 76 degrees.

Since OA and OB are radii of the same circle, triangle AOB is an isosceles triangle with OA = OB.

In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, angle OAB = angle OBA.

So, angle OAB = 76 degrees.

The sum of angles in a triangle is 180 degrees. In triangle AOB, the sum of angles is angle OAB + angle OBA + angle AOB = 180 degrees.

76 degrees + 76 degrees + angle AOB = 180 degrees

152 degrees + angle AOB = 180 degrees

angle AOB = 180 degrees - 152 degrees

angle AOB = 28 degrees.

Ответ: 28°