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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.
∠R + ∠Q = 180° ....(Interior angles)
⇒ `x° + (x°)/(4)` = 180°
⇒ 4x° + x° = 180° x 4
⇒ 5x° = 180° x 4
⇒ x° = `(180° xx 4)/(5)`
⇒ x° = 144° = ∠R
⇒ `x°/(4) = (144°)/(4)` = 36° = ∠Q
⇒ ∠P = ∠R = 144 ....(Opposite angles of a parallelogram are equal)
∠S = ∠Q = 36°.
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