Question

Given: m arc IV =140°, m arc VK =30°, m∠ISV=135° Find: m∠VPL

Answer 1

`m<VPL=80\°`

Explanation:

step 1

Find the measure of arc PK

we know that

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

Let

x------> the measure of arc IV

y ------> the measure of arc PK

`m<ISV=(1)/(2)(x+y)`

substitute the values and solve for y

`135\°=(1)/(2)(140\°+y)`

`270\°=(140\°+y)`

`y=270\°-140\°=130\°`

The measure of arc PK is
`130\°`

step 2

Find the measure of angle VPL

we know that

The inscribed angle measures half that of the arc comprising

Let

z------> the measure of arc VK

y ------> the measure of arc PK

`m<VPL=(1)/(2)(z+y)`

substitute the values

`m<VPL=(1)/(2)(30\°+130\°)=80\°`