Answer:
[tex]m<VPJ=140\°[/tex]
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
[tex]x+y=360\°[/tex] -----> equation A
[tex]x=\frac{7}{2}y[/tex] -----> equation B
Substitute equation B in equation A
[tex]3.5y+y=360\°[/tex]
[tex]4.5y=360\°[/tex]
[tex]y=80\°[/tex]
Find the value of x
[tex]x=\frac{7}{2}(80)=280\°[/tex]
step 2
Find the measure of angle VPJ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<VPJ=\frac{1}{2}(x)[/tex]
substitute
[tex]m<VPJ=\frac{1}{2}(280\°)=140\°[/tex]
