# In a triangle, ABC is inscribed in a circle centered at point O

September 29, 2021 | education

| **In a triangle, ABC is inscribed in a circle centered at point O, Calculate the degree measure of the angle AOC if it is 50 degrees greater than the degree measure of the angle ABC**

The inner angle ABC of the triangle ABC is the angle inscribed in the circle, which rests on the arc AC, then the degree measure of the arc AC is equal to two degree measures of the inscribed angle.

Arc AC = 2 * 50 = 100.

The sought, central angle AOC also rests on the arc AC, then the angle AOB is equal to the degree measure of the arc AC. Angle AOC = 100.

Answer: The AOC angle is 100.

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