Question

Point C is the center of the circle. The measure of angle ACB is 3x + 120. Arc AB measures 65x – 4. Find the measure of arc AB.

Answer 1

Answer:

The measure of arc AB is 126°.

Step-by-step explanation:

It is given that point C is the center of the circle. The measure of angle ACB is 3x + 120. Arc AB measures 65x – 4.

The measure of central angle is equal to the measure of arc.

$3x+120=65x-4$

Solve this equation for x.

$120+4=65x-3x$

$124=62x$

Divide both the sides by 62.

$\frac{124}{62}=x$

$2=x$

The value of x is 2.

The measure of arc AB is

$65x-4=65(2)-4\Rightarrow 130-4=126$

Therefore the he measure of arc AB is 126°.

Answer 2

In a circle The measurement of a CENTRAL ANGLE (vertex C) is equal to the measurement of the arc intercepted:

65x-4 = 3x+120 ===> 62x=124 & x= 2, hence the arc = 2