Question

What is the measure of AC ? (First Picture)

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What is the measure of BC ? (Second Picture)
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Answer 1

Part 1)
`arc\ AC=33\°`

Part 2)
`arc\ BC=130\°`

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<ABC=(1)/(2)(arc\ AC)`

substitute the values and solve for x

`2.5x+4=(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<BDC=(1)/(2)(arc\ BC)`

substitute the values

`65\°=(1)/(2)(arc\ BC)`

`2*65\°=(arc\ BC)`

`arc\ BC=130\°`