Question

PQ⊥PS , m∠QPR=7x−9, m∠RPS=4x+22
Find : m∠QPR

Answer 1

Given:

It is given that,

PQ ⊥ PS and

∠QPR = 7x-9

∠RPS = 4x+22

To find the value of ∠QPR.

Formula

As per the given problem PR lies between PQ and PS,

So,

∠QPR+∠RPS = 90°

Now,

Putting the values of ∠RPS and ∠QPR we get,

`7x-9+4x+22 = 90`

or,
`11x = 90-22+9`

or,
`11x = 77`

or,
`x = (77)/(11)`

or,
`x = 7`

Substituting the value of
`x = 7` in ∠QPR we get,

∠QPR =
`7(7)-9`

or, ∠QPR =
`40^\circ`

Hence,

The value of ∠QPR is 40°.