A circle with center O is circumscribed about obtuse triangle ABC. Angle AOC is 140 °.
| September 12, 2021 | education
A circle with center O is circumscribed about obtuse triangle ABC. Angle AOC is 140 °. What is the obtuse angle of triangle ABC?
The central angle AOC rests on the arc ABC. Then the degree measure of the arc BAC is equal to the degree measure of the angle AOC.
Arc ABC = 140.
The degree measure of the full circle is 360, then the large arc AC = 360 – 140 = 220.
The inscribed angle ABC is based on the arc AC, then the angle ABC is equal to half the degree measure of the arc AC.
Angle ABC = 220/2 = 110.
Answer: The obtuse angle of triangle ABC is 110.
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