If lines pq and rs intersect at point t

Asked by admin @ in Math viewed by 408 People

"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"

Answered by admin @


Vertically opposite angles:


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


_____________________________________________________________


 


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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