The image shows a circle with center O and points A, B, and C on the circumference. Angle AOC is marked as 78 degrees. What is the measure of angle ABC?

Analysis:

• The angle AOC is a central angle subtended by the arc AC.
• The angle ABC is an inscribed angle subtended by the same arc AC.
• The measure of an inscribed angle is half the measure of its corresponding central angle.
• Therefore, the measure of angle ABC is half the measure of angle AOC.

Calculation:

Angle ABC = (1/2) * Angle AOC

Angle ABC = (1/2) * 78 degrees

Angle ABC = 39 degrees

Ответ: 39°