Question

In the given figure, PQ || RS, Prove that <QPT - <TRS= <PTR​

Answer 1

Answer:

 PQ || RS

∠QPT = 100°

∠TRS = 110°

To Find : ∠PTR

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°)

PQ || RS

Draw TU || PQ || RS

∠QPT + ∠PTU = 180°   Interior angles

=>  100°  + ∠PTU = 180°

=> ∠PTU = 80°

∠TRS + ∠RTU = 180°   Interior angles

=>  110°  + ∠RTU = 180°

=> ∠RTU = 70°

∠PTR =   ∠PTU +  ∠RTU

=> ∠PTR =   80°  + 70°

=> ∠PTR =   150°

hope it was helpful

Step-by-step explanation: