Question

In quadrilateral PQRS , angle P = angle R = 108 , angle Q = angle S = 72 .State which pair of sides of those given below is parallel .


Side PQ and Side QR

Side PQ and Side SR

Side SR and Side SP

Side PS and Side PQ

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Answer 1

Given : In quadrilateral PQRS , ∠P =∠R = 108 ,∠Q = ∠S = 72 .

To Find :

State which pair of sides of those given below is parallel .

Side PQ and Side QR

Side PQ and Side SR

Side SR and Side SP

Side PS and Side PQ

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent. ( Equal in Measure)

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Co-Interior angles are supplementary. ( adds up to 180°)

Converse are also True

∠P =∠R = 108° ,∠Q = ∠S = 72° .

∠P + ∠Q = 108° + 72° = 180°

Co-Interior angles are supplementary

Hence PS || QR

∠P + ∠S  = 108° + 72° = 180°

Co-Interior angles are supplementary

Hence PQ || SR

Side PQ and Side SR  are  parallel

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