PQRS is a cyclic quadrilateral. If angle P is three times the angle R

| PQRS is a cyclic quadrilateral. If angle P is three times the angle R and angle S is five times the angle Q, then the sum of the angles Q and R is:

A. 65°

B. 70°

C. 72°

D. 75°

Right Answer is: D

SOLUTION

In cyclic quadrature opposite angles are supplementary angles so,

P+R=180°

3α+α=180°

4α=180°

α=45°

And Q+S=180°

5β+β=180°

6β=180°

β=30°

Q+R=β+α

=30°+45°

=75°

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