In a circle with center O, a cyclic quadrilateral ABCD is inscribed. If the measure of the angle ∠ADC=110°, what is the measure of the angle ∠AOC?
Show answer & explanation
Correct answer: C
Explanation
Given:
∠ADC = 110°
Formula:
The sum of opposite angles in a cyclic quadrilateral = 180°
Angle at the center = 2 × angle at the circumference
∠ABC + ∠ADC = 180°
∠ABC + 110° = 180°
∠ABC = 70°
∠AOC = 2 × ∠ABC
∠AOC = 2 × 70°
∠AOC = 140°