Question

1. Given: m arc PIV= 7/2 m arc PKV

Find: m∠VPJ

Answer 1

`m<VPJ=140\°`

Explanation:

step 1

Find the measure of arc PIV

Let

x------> the measure of arc PIV

y-----> the measure of arc PKV

`x+y=360\°` -----> equation A

`x=(7)/(2)y` -----> equation B

Substitute equation B in equation A

`3.5y+y=360\°`

`4.5y=360\°`

`y=80\°`

Find the value of x

`x=(7)/(2)(80)=280\°`

step 2

Find the measure of angle VPJ

we know that

The inscribed angle measures half that of the arc comprising

so

`m<VPJ=(1)/(2)(x)`

substitute

`m<VPJ=(1)/(2)(280\°)=140\°`