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, $x = \frac{77}{11}$

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°.