Question

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

Answer 1

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.