Question

ID
the given figure (adjacent) show that
POU TU. Give reasons.
PL
569
26
150*
30°
→ 5
R.​

Answer 1

Step-by-step explanation:

angle PQR=56°

Angle QRS= 26°+30°

=56°

angle PQR=Angle QRS

Alternate angles are equal so PQ parallel to RS-->I

RS parallel to TU sum of co interior angles = 150°+30°=180°----> II

from I, II

PQ parallel to TU

Answer 2

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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