Given that angle BOC = 130 degrees, find the measure of angle AOB.

Solution:

The angles AOB and BOC form a straight line AD. Therefore, they are supplementary angles, meaning their sum is 180 degrees.

We are given that \( \angle BOC = 130^{\circ} \).

The relationship between the angles is:

\( \angle AOB + \angle BOC = 180^{\circ} \)

Substitute the given value of \( \angle BOC \):

\( \angle AOB + 130^{\circ} = 180^{\circ} \)

To find \( \angle AOB \), subtract 130 degrees from both sides:

\( \angle AOB = 180^{\circ} - 130^{\circ} \)

\( \angle AOB = 50^{\circ} \)

Ответ: \( \angle AOB = 50^{\circ} \).