Question

"Question 1 In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

Class 9 - Math - Lines and Angles Page 107"

Answer 1

I think you understand it...

Answer 2

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

 

Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

 

Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.

 

The two axioms given above together are called the linear pair axioms.

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Solution:

 

Given,
∠SPR = 135° and ∠PQT = 110°

A.T.Q

∠SPR +∠QPR = 180° (by Linear pair axiom.)

⇒ 135° +∠QPR = 180°

⇒ ∠QPR = 180° - 135°

⇒ ∠QPR = 45°

∠PQT +∠PQR = 180° (by Linear pair axiom.)

⇒ 110° +∠PQR = 180°

⇒ ∠PQR = 70°

Now,
∠PQR +∠QPR + ∠PRQ = 180° (Sum of the interior angles of the triangle.)
⇒ 70° + 45° + ∠PRQ = 180°
⇒ 115° + ∠PRQ = 180°

⇒ ∠PRQ = 65°

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