Question

What is the measure of AC?

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°
Image shows a circle with angle A B C inscribed in a circle. Angle B measures 4 x minus 5.5 degrees. Arc A C measures 3 x plus 9 degrees.

Answer 1

Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

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

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

For more explanation, refer the following link:

https://brainly.com/question/8841969

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