Answer:
∠PQS = ∠PQR+∠RQS
x²-5 = 45+5x
x²-5-45-5x=0
x²-5x-50=0
b²-4ac = (-5)²-4(1*-50)= 225
Δ=225; √Δ=15
Δ is strictly positive, the equation x²−5x−50=0 admit two solutions.
(-b-√Δ)/2a = (5-15)/2 = -10/2=-5
(-b+√Δ)/2a = (5+15)/2 =10
x = -5 or 10
a measurement is never negative, x= 10°
∠PQS = x²-5 = 10²-5 = 95°
we check :
∠PQS= (95°)=∠PQR+∠RQS = 45+5x = 45*5*10 =95°