PQRS is a cyclic quadrilateral. If ∠P is four times ∠R and ∠S is three times ∠Q, then sum of the measures of ∠S and ∠R will be:

171°

Here,

PQRS is a cyclic quadrilateral

∠P = 4∠R 

∠S = 3∠Q

We know that,

∠P + ∠R = 180° and

 ∠Q + ∠S = 180°

Let the  ∠R and ∠Q be x and y respectively.

According to the question,

∠P =  4x   and

 ∠S = 3y

∠P + ∠R = 180°

= 4x + x = 180°

= x = 36°

Also,

∠Q + ∠S = 180°

= y + 3y = 180°

= y = 45°

So the value of∠Q + ∠R = 36° + 45° = 81°