Question

33. In fig 6.42 if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠ RPT = 95° and∠ TSQ = 75°, i) ∠ SQT. =------- ii) ∠ STQ=---------
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Answer 1

Answer:

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∘