Question

What is the measure of AC ? (First Picture)

Answer 1

Answer:

Part 1) $arc\ AC=33\°$

Part 2) $arc\ BC=130\°$

Step-by-step explanation:

Part 1) What is the measure of AC ?

we know that

The inscribed angle is half that of the arc it comprises.

so

$m$

substitute the values and solve for x

$2.5x+4=\frac{1}{2}(7x-2)$

$5x+8=(7x-2)$

$7x-5x=8+2$

$2x=10$

$x=5\°$

Find the measure of arc AC

$arc\ AC=7x-2=7(5)-2=33\°$

Part 2) What is the measure of BC ?

we know that

The inscribed angle is half that of the arc it comprises.

so

$m$

substitute the values

$65\°=\frac{1}{2}(arc\ BC)$

$2*65\°=(arc\ BC)$

$arc\ BC=130\°$