Answer:
The measure of angle VPJ is [tex]140\°[/tex]
Step-by-step explanation:
Let
x-----> the measure of arc PIV
y-----> the measure of arc PKV
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<VPJ=\frac{1}{2}(x)[/tex]
[tex]x=3.5y[/tex] -----> equation A
[tex]x+y=360\°[/tex] -----> equation B
substitute equation A in equation B
[tex]3.5y+y=360\°[/tex]
[tex]4.5y=360\°[/tex]
[tex]y=80\°[/tex]
Find the value of x
[tex]x=3.5(80\°)=280\°[/tex]
Find the measure of angle VPJ
[tex]m<VPJ=\frac{1}{2}(280\°)=140\°[/tex]
