Question

25 POINTS FOR ANSWER AND EXPLANATION:
Given: m IP + m VK = 86°
Find: m∠KSP

Answer 1

The measure of angle KSP is
`137\°`

Explanation:

step 1

Find the measure of angle ISP

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

`m<ISP=(1)/(2)(arc\ VK+arc\ IP)`

we have

`(arc\ VK+arc\ IP)=86\°`

substitute

`m<ISP=(1)/(2)(86\°)=43\°`

step 2

Find the measure of angle KSP

we know that

`m<ISP+m<KSP=180\°` ----> by supplementary angles

we have

`m<ISP=43\°`

substitute

`43\°+m<KSP=180\°`

`m<KSP=180\°-43\°=137\°`