Question

In The figure given below, m||n, TU||PQ and ∠PQ=75ᵒ, ∠QR =30ᵒ. Find the angles∠SOP,∠PQR,∠TUSQ ∠STU.

Answer 1

Given :  m || n  and TU||PQ

∠SPQ=75ᵒ, ∠QOR =30ᵒ.

To Find : ∠ SOP, ∠ PQR, ∠TUQ & ∠STU.​

Solution:

∠QOR = 30°

∠SOP = ∠QOR  ( Vertically opposite angles)

=> ∠SOP =  30°

∠PQR =  ∠SPQ  ( Alternate angle)

∠SPQ=75°

=> ∠PQR = 75°

∠TUQ = ∠PQR   ( corresponding angles)

∠TUQ =  75°

∠STU + ∠SPQ  = 180°    Interior angles

=> ∠STU  + 75° = 180°    

=>  ∠STU   = 105°  

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°)

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