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Q.

In the given figure l, m and n are parallel lines intersected by transversal p at X,Y and Z respectively. Find ∠1, ∠2 and ∠3.


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a

∠1=110 °, ∠2=110 ° , ∠3=110 °

b

∠1=100 °, ∠2=100 ° , ∠3=120 °

c

∠1=90 °, ∠2=90 ° , ∠3=90 °

d

∠1=120 °, ∠2=120 ° , ∠3=120 ° 

answer is D.

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Detailed Solution

It is given that l, m and n are parallel lines intersected by transversal p at points, X, Y and Z respectively.
Question ImageWe can observe from the figure that ∠4 and 60° are on a straight line.
We know that, linear pair of angles theorem states that the measure of a straight-line angles is 180 °  .
So,
∠4+ 60 ° = 180 °  
⇒∠4= 180 ° − 60 °   ⇒∠4= 120 °  
We can also observe from the figure that,
∠4=∠1  (Corresponding angles)
Hence, we can write that,
∠4=∠1= 120 °  
  ∠1=∠2= 120 °  
We know that, vertical opposite angle, angles that are opposite each other when two lines intersects.
So, ∠3=∠2= 120 °  
The values of angles ∠1,∠2,∠3   are 120 ° , 120 ° , 120 °  respectively.
Hence, the correct option is 1.
 
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In the given figure l, m and n are parallel lines intersected by transversal p at X,Y and Z respectively. Find ∠1, ∠2 and ∠3.