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In the given figure, a transversal n cuts two lines l and m such that $∠ 2 = 65 °$ and $∠ 8 = 65 °$ . State if the given statement is true or false with reference to the given conditions. “l and m are parallel lines.”

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True

False

answer is A.

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Detailed Solution

It is given that, a transversal n cuts two lines l and m such that

∠ 2 = 65 °

and

∠ 8 = 65 °

We can observe from figure that,

∠ 2 = ∠ 4

(Vertically Opposite angle)
Hence, we can write that,

∠ 2 = ∠ 4 = 65 °

(As the value of angle 2 is given as 65°)
By observing the figure, we can also write that,

∠ 8 = ∠ 6 = 65 °

Therefore,

∠ 4 = ∠ 6

.
Hence,

l ∥ m

.
Yes, the lines

l

and

m

are parallel.
Hence, the statement is true i.e., “l and m are parallel lines.”
The correct option is 1.

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