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Question
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
∠P = 100°, ∠Q = 80°, ∠R = 95°
Solution
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
∠P =100° , ∠Q = 80° ,∠R = 100°
By angle sum property of a quadrilateral, we get:
∠P + ∠Q + ∠R +∠S = 360°
100° + 80° + 100° +∠S = 360°
280° +∠S 360°
∠S = 80°
Clearly, ∠P = ∠R
And ∠Q = ∠S
Thus we have PQRS a quadrilateral with opposite angles are equal.
Therefore,
PQRS is a parallelogram.
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