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

Mathematics

2 answers:

liq [111]3 years ago

8 0

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

mart [117]3 years ago

5 0

Answer:

C. $56^{\circ}$

Step-by-step 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:

$m\angle BAC=\frac{1}{2}\times \text{ Measure of arc AC}$

$28^{\circ}=\frac{1}{2}\times \text{ Measure of arc AC}$

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

$2*28^{\circ}=\frac{1}{2}*2\times \text{ Measure of arc AC}$

$56^{\circ}=\text{ Measure of arc AC}$

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

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