Question

What is the measure of (arc) BC?

A. 55

B. 110

C. 48

D. 96

Answer 1

Angle BAC is the inscribed angle, therefore it is equal to half the arc AB ⇒

arc AB = 2*48 = 96°

Answer 2

(D)
`96^(\circ)=(arc)BC`

Explanation:

It is given from the figure that m∠BAC=48° and arcAC=110°.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Now, using the above property, we have

`m{\angle}BAC={(1)/(2)}(arc)BC`

Substituting the given values, we get

`48^(\circ)=(1)/(2)(arc)BC`

`96^(\circ)=(arc)BC`

Thus, the measure of the arc BC is 96 degrees.

Hence, option D is correct.