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

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,

or,

or,

or,

or,

Substituting the value of in ∠QPR we get,

∠QPR =

or, ∠QPR =

Hence,

The value of ∠QPR is 40°.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3