Examine circle C,

Question

with central angle, ∠DCA,
inscribed angle, ∠AQD,
and intercept AD⌢.
Circle C as described in the text.If the measure of AD⌢=78∘,
what is m∠AQD?
Responses

78∘
78 degrees

39∘
39 degrees

156∘
156 degrees

12∘

Answer 1

39∘

The inscribed angle (∠AQD) is half of the intercepted arc (AD⌢), so if the intercepted arc is 78°, then the inscribed angle is half of that, which is 39°.