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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 =85°, ∠Q = 85°, ∠R = 95°
Solution
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
∠P =85°, ∠Q = 85°, ∠R = 95°
By the angle sum property of a quadrilateral, we get:
∠P + ∠Q + ∠R + ∠S = 360
8585 + 95 + ∠S = 360
265 + ∠S = 360
∠S = 95
Clearly, ∠P ≠ ∠R
And ∠Q ≠ ∠S
Thus, we have PQRS a quadrilateral with opposite angles that are not equal.
Therefore,
PQRS is not a parallelogram.
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