Question

In the given figure (adjacent) show that PQ TU Give reasons
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Answer 1

Given : ∠PQR = 56° , ∠QRT = 26° , ∠SRT  = 30° , ∠RTU = 150°

To Find : show that  PQ ||  TU

Solution  :

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

• Corresponding angles are congruent.  

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

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

If two lines are parallel to third line then lines are parallel  to each other

∠UTR + ∠SRT = 150° + 30° = 180°

As Interior angles are supplementary

Hence TU || RS

∠QRS = ∠QRT + ∠SRT

=> ∠QRS = 26° + 30°

=> ∠QRS = 56°  

∠PQR = 56°

Hence ∠PQR = ∠QRS

Interior   Alternate angles are congruent

Hence PQ || RS

TU || RS

PQ || RS

=> PQ ||  TU

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