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:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 40.5 °.
We know that,
Average = sum of numbers/Total numbers
Now, According to the question
⇒ ∠P = 4 × ∠R
⇒ ∠P : ∠R = 4 : 1
By using the property
⇒ ∠P + ∠R = 180°
⇒ 4x + x = 180°
⇒ 5x = 180°
⇒ x = 36°
⇒ ∠R = 36°
Now,
⇒ ∠S = 3 × ∠Q
⇒ ∠S : ∠Q = 3 : 1
⇒ 3y + y = 180°
⇒ 4y = 45
⇒ ∠Q = 45
The average of ∠R and ∠Q is
⇒ (∠R + ∠Q)/2 = (36 + 45)/2 = 81/2 = 40.5
So, The average of ∠R and ∠Q is 40.5