Question

circumscribed angle aec intercepts circle o at a and c. central angle aoc also intercepts circle o at a and c. if ∠aoc measures 87°, what is the measure of ∠aec? use the keypad to enter the answer in the box. include the correct symbol for the units of measure.

Explanation:

Step1: Recall the relationship between circumscribed angle and central angle

The measure of a circumscribed angle \( \angle AEC\) and the central angle \( \angle AOC\) that intercepts the same arc satisfy the formula \( \angle AEC = 180^{\circ}-\angle AOC\) (when the angle is formed outside the circle by two tangents).

Step2: Substitute the given value of \( \angle AOC\)

Given \( \angle AOC = 87^{\circ}\), substitute into the formula: \( \angle AEC=180^{\circ}- 87^{\circ}\)

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Answer:

\(93^{\circ}\)