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Question
In the following figures, find the remaining angles of the parallelogram
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Solution
PQRS is a parallelogram with all sides equal and opposite sides parallel.
Hence, PQRS is a Rhombus.
Diagonals of a Rhombus bisect each other.
In ΔPOS,
∠OSP + ∠SPO + ∠POS = 180°
⇒ x + 70° + 90° = 180°
⇒ x = 20°
In ΔQSP,
PS = PQ
⇒ ∠QSP = ∠PQS = x = 20°
And,
∠QSP + ∠PQS + ∠SPQ = 180°
⇒ 20° + 20° + ∠SPQ = 180°
⇒ ∠SPQ = 140°
⇒ ∠SPQ = 140° ....(Opposite angles are equal)
Now,
∠SPQ + ∠SR = 180°
⇒ 140° + PSR = 180°
⇒ ∠PSR = 40°
⇒ ∠PQR = 40° ....(Opposite angles are equal)
Hence,
∠P =∠R = 140° and ∠S = ∠Q = 40°.
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