Answer :
Answer:
Measure of angle 'VPJ' is 140 degrees.
Step-by-step explanation:
Given:
Measure of arc 'PIV' and measure of arc 'PKV'.
'PIV' = 7/2 times of 'PKV'
Lets say that PKV is 'x'.
⇒ [tex]m(PIV)=\frac{7}{2} \times x[/tex]
⇒ [tex]m(PIV)=3.5x[/tex]
Note:
A full circle has an arc angle measure of 360.
So,
⇒ [tex]3.5x+x=360[/tex]
⇒ [tex]4.5x=360[/tex]
⇒ [tex]x=\frac{360}{4.5}[/tex]
⇒ [tex]x=80[/tex]
The measure of arc 'PKV' = 80 degrees.
We have to find angle 'VPJ' that is having a linear pair with angle 'VPL'.
So before finding we 'VPJ' have to find 'VPL'.
And
According to the theorem:
The angle formed by the tangent and the chord is half the measure of the intercepted arc.
Then.
⇒ [tex]\angle VPL=\frac{m\ arc\ (PKV)}{2}[/tex]
⇒ [tex]\angle VPL=\frac{80}{2}[/tex]
⇒ [tex]\angle VPL=40[/tex] degrees
⇒ And from linear pair .
⇒ [tex]m\angle VPL +m \angle VPJ =180[/tex]
⇒ [tex]40 +m \angle VPJ =180[/tex]
⇒ [tex]m \angle VPJ =180-40[/tex]
⇒ [tex]m \angle VPJ =140[/tex] degrees.
So measure of angle 'VPJ' is 140 degrees.
