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# 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° - Mathematics

Answer in Brief

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°

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#### 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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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 13 Quadrilaterals
Q 3.1 | Page 71
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