Question

PQRS is a kite.∠P = 70°, 

∠S = 90.5°, ∠R equals

(a) 99° 

(b) 91° 

(c) 111° 

(d) 109°

Answer 1

(d) 109°

In a kite, the two pairs of adjacent sides are equal, i.e., PS = PQ and SR = RQ 

In ΔPSQ, 

∠PSQ =∠PQS = \(\frac{180°-70°}{2}=\frac{110°}{2}\) = 55°

∴ ∠QSR = 90.5° – 55° = 35.5°

⇒ ∠RQS = ∠QSR = 35.5°      (∵RQ = RS) 

In ΔSRQ, 

∠R +∠RQS +∠QSR = 180° 

⇒ ∠R + 35.5° + 35.5° = 180° 

⇒ ∠R = 180° – 71° = 109°.