Question

Which is larger? The measure of a central angle of a circle that intercepts a 68 degree arc of the measure of an inscribed angle of a circle that intercepts a 68 degree arc. Explain

Answer 1

The measure of a central angle of a circle that intercepts a 68° arc

Explanation:

Recall the inscribed angle theorems:

Measure of central angle = measure of intercepted arc

Measure of inscribed angle = ½(measure of intercepted arc)

Therefore,

The measure of a central angle that intercepts a 68° arc = 68°

Measure of an inscribed angle of a circle that intercepts a 68° arc = ½(68°) = 34°

Therefore, the larger would be:

The measure of a central angle of a circle that intercepts a 68° arc