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:
Answer & explanation
Correct answer: option 3
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°