Question

What is measure of Arc AC if the m ∠BAC = 28°?

28 degrees
14 degrees
56 degrees
152 degrees

Answer 1

14 degrees. It equals half the intercepted arc.
(See attached graphic)

Answer 2

C.
`56^(\circ)`

Explanation:

We have been given an image of a circle. We are asked to find the measure of arc AC.

We will use tangent-secant theorem, which states that the angle formed by a tangent to a circle and a chord is equal to half the angle measure of the intercepted arc.

Using above theorem we can set an equation to find measure of arc AC as:

`m\angle BAC=(1)/(2)* \text{ Measure of arc AC}`

`28^(\circ)=(1)/(2)* \text{ Measure of arc AC}`

Multiplying both sides of our equation by 2, we will get,

`2*28^(\circ)=(1)/(2)*2* \text{ Measure of arc AC}`

`56^(\circ)=\text{ Measure of arc AC}`

Therefore, the measure of arc AC is 56 degrees and option C is the correct choice.