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Elena-2011 [213]
3 years ago
13

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

Mathematics
1 answer:
Serhud [2]3 years ago
6 0

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'.

⇒ m(PIV)=\frac{7}{2} \times 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=\frac{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=\frac{m\ arc\ (PKV)}{2}

⇒ \angle VPL=\frac{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.

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