Question

PQRS is a kite and angle P and angle R equal. If angle RPS = 70° and angle RQS = 65°, find (a) angle QRS (b) angle PSR?​

Answer 1

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Answer 2

Given :  PQRS is a kite and ∠P and ∠R equal. If angle RPS = 70° and angle RQS = 65°,

To find  : (a) ∠QRS (b) ∠PSR

Solution:

In Kite:

Diagonals are perpendicular to each other

Two pairs of adjacent sides are equal.

One pair of opposite angles are equal.

∠P and ∠R equal.

Hence PS = RS       and  PQ = QR

=> ∠PRS = ∠RPS

=> ∠PRS = 70°      ( as angle opposite to Equal sides are equal in a triangle)

∠PRQ + 90° + 65° =  180°  ( sum of angles of a triangle)

=> ∠PRQ = 25°

∠QRS = ∠PRQ + ∠PRS

=> ∠QRS =  25° +  70°  

=> ∠QRS = 95°

in ΔPSR

∠PRS + ∠PSR + ∠RPS = 180°

=>  70°  + ∠PSR + 70° = 180°

=>  ∠PSR = 40°

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