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

PKV

Find: m∠VPJ

1 Answer

7 votes

Answer:

Measure of angle 'VPJ' is 140 degrees.

Explanation:

Given:

Measure of arc 'PIV' and measure of arc 'PKV'.

'PIV' = 7/2 times of 'PKV'

Lets say that PKV is 'x'.


m(PIV)=(7)/(2) * x


m(PIV)=3.5x

Note:

A full circle has an arc angle measure of 360.

So,


3.5x+x=360


4.5x=360


x=(360)/(4.5)


x=80

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.


\angle VPL=(m\ arc\ (PKV))/(2)


\angle VPL=(80)/(2)


\angle VPL=40 degrees

⇒ And from linear pair .


m\angle VPL +m \angle VPJ =180


40 +m \angle VPJ =180


m \angle VPJ =180-40


m \angle VPJ =140 degrees.

So measure of angle 'VPJ' is 140 degrees.

Given: measure of arc PIV = 7/2 times measure of arc PKV PKV Find: m∠VPJ-example-1
Given: measure of arc PIV = 7/2 times measure of arc PKV PKV Find: m∠VPJ-example-2
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