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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.

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∠1=110 °, ∠2=110 ° , ∠3=110 °

∠1=100 °, ∠2=100 ° , ∠3=120 °

∠1=90 °, ∠2=90 ° , ∠3=90 °

∠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 Image

We 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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