Question

"Question 4 In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

Class 9 - Math - Lines and Angles Page 107"

Answer 1

Vertically opposite angles:

When two line intersect each other at a point then there are two pairs of vertically opposite angles.

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Solution:

 

Given: ∠PRT= 40°, ∠RPT=95°, ∠TSQ=75°

 

In △PRT,

 

∠PTR+∠PRT+∠RPT=180° 

 

 [sum of interior angles of a triangle is 180°].

 

⇒∠PTR+40∘+95∘=180∘

 ⇒∠PTR+135∘=180∘ ⇒∠PTR=180∘−135∘

 ⇒∠PTR=45∘

⇒∠QTR=∠PTR=45∘  

 (vertically opposite angles)

 

In △TSQ,

∠QTS+∠TSQ+∠SQT=180∘   

[sum of interior angles of a triangle is 180∘].

 

45∘+75∘+∠SQT=180∘ ⇒120∘+∠SQT=180∘ 

⇒∠SQT=180∘−120∘

 ⇒∠SQT=60∘

 

Hence, ∠SQT=60∘

 

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Answer 2

yess, in∆PRT ,
<PTR+<PRT+<RPT= 180°
( °.° a triangles all three angles equal is 180° )
=> <PTR+40°+95°=180°
=> <PTR = 180°-135° = 45°
=> < QTS=<PTR = 45° ( Opposite angle )
in ∆TSQ
<QTS+<TSQ+<SQT=180°
=> 45°+75°+<SQT=180°
=> 120°+ <SQT= 180°
=> <SQT= 180°-120°= 60°
hopes I helped