In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?

Correct option is D

Given:
In quadrilateral PQRS, bisectors of ∠R and ∠S meet at T.
∠STR = 22.5°
Ratio of ∠P : ∠Q = 4 : 5
Formula Used:
In a quadrilateral, the angle formed by the intersection of the angle bisectors of two consecutive angles is equal to half the sum of the other two angles.
∠STR = $$\frac{∠P + ∠Q}{2}$$​​
Solution: 

Substitute the value of ∠STR into the formula:
22.5° = $$\frac{∠P + ∠Q}{2}$$​​
∠P + ∠Q = 22.5° × 2 = 45°
Let ∠P be 4x and ∠Q be 5x.
4x + 5x = 45°
9x = 45°
x = 5°
We need to find the difference between ∠Q and ∠P:
Difference = 5x - 4x = x
Difference = 5°
Final Answer
So the correct answer is (d)