Given: measure of arc PIV = 7/2 times measure of arc PKV

PKV

Find: m∠VPJ

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'.

⇒

⇒

Note:

A full circle has an arc angle measure of 360.

So,

⇒

⇒

⇒

⇒

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.

⇒

⇒

⇒ degrees

⇒ And from linear pair .

⇒

⇒

⇒

⇒ degrees.

So measure of angle 'VPJ' is 140 degrees.

-81 -56 -27 0 81

step-by-step explanation: