PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:

Solution (By Examveda Team)

Given that
∠P = 4∠R
∠S = 3∠Q
∠P + ∠R = 180°
4β + β = 180°
5β = 180°
β = 36°
∠S + ∠Q = 180°
3α + α = 180°
4α = 180°
α = 45°
Average of ∠Q and ∠R $$ = \frac{{{{36}^ \circ } + {{45}^ \circ }}}{2} = {40.5^ \circ }$$