Question

In a cyclic quadrilateral PQRS, ∠P is double its opposite angle and difference between the other two angles is onethird of ∠P. The minimum difference between any two angles of this quadrilateral is 

(a) 30° 

(b) 10° 

(c) 20° 

(d) 40°

Answer 1

(b) 10°.

Given, ∠P = 2∠R                ...(i) 

Also, ∠P + ∠R = 180°         ...(ii) 

∠Q + ∠S = 180°                  ...(iii) 

∴ From (i) and (ii) 

⇒ ∠R = 60° 

⇒ ∠P = 120° 

Also, given  ∠Q −∠S =\(\frac13\)∠P = \(\frac13\) x 120°= 40°        ...(iv) 

Solving (iii) and (iv) simultaneously, we get 

∠Q = 110°, ∠S = 70° 

∴ Minimum difference between any two angles of the quadrilateral is 10°.