giving brainliest !!!!!!

We are given that lines [tex]PQ[/tex] and [tex]PS[/tex] are perpendicular lines, meaning they intersect and each other, and as a result, create a right angle ([tex]90[/tex]).

With that being said, let's add the expressions representative of the two angles and set them equal to [tex]90[/tex] degrees:

[tex]7x-9+4x+22=90[/tex]

Combine like terms:

[tex]11x+13=90[/tex]

Subtract 13 from both sides of the equation:

[tex]11x=77[/tex]

Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]11[/tex]:

[tex]x=7[/tex]

Now, let's substitute this into the expression of angle [tex]QPR[/tex]:

[tex]7(7)-9[/tex]

[tex]=40[/tex]

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You can check your work by substituting the value of [tex]x[/tex] into the other expression, and then adding that answer with our initial answer to make sure it equals [tex]90[/tex] degrees:

[tex]4(7)+22[/tex]

[tex]28+22=50[/tex]

[tex]40+50=90[/tex]

Since the two angles add up to 90, our answer is correct!