Question

Point D is the center of the given circle.What is the measure of arc AC?

Answer 1

ANSWER


`D. \: \: 96\degree`

Step-by-step explanation

The measure of angle ABC is 48°.

Angle about the center is twice the angle about the edge.

The measure of angle ADC is twice the measure of angle ABC.

This implies that,


`m \: < \: ADC=2(m \: < \: ABC)`

We substitute to obtain,


`m \: < \: ADC=2(48 \degree)`

We simplify to get,


`m \: < \: ADC=96 \degree`

Hence the measure of arc AC is 96°.

Therefore the correct answer is option D.

Answer 2

∠ABC is an inscribed angle.
In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. m∠ABC = 48° ⇒
measure of arc AC = 2*m∠ABC = 2 * 48 = 96°.