Question

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

Find: m∠VPJ

Answer 1

Answer:

$m<VPJ=140\°$

Step-by-step 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

$x=\frac{7}{2}y$ -----> equation B

Substitute equation B in equation A

$3.5y+y=360\°$

$4.5y=360\°$

$y=80\°$

Find the value of x

$x=\frac{7}{2}(80)=280\°$

step 2

Find the measure of angle VPJ

we know that

The inscribed angle measures half that of the arc comprising

so

$m<VPJ=\frac{1}{2}(x)$

substitute

$m<VPJ=\frac{1}{2}(280\°)=140\°$