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Tell whether the following statement is true or false:

In Figure, p is a transversal to lines m and n, $∠ 2 = 120 °$ and $∠ 5 = 60 °$ . Then, m || n.

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True

False

answer is A.

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Detailed Solution

Given a figure in which p is a transversal to lines m and n,

∠ 2 = 120 °

and

∠ 5 = 60 °

In Fig., p is a traversal to lines m and n, 2 = 120^∘ and 5 = 60^∘ . Prove that m∥ n.

Linear pair property states that the sum of angles of a linear pair is always equal to 180°.
Calculate

∠ 1

using linear angle property.

∠ 1

and

∠ 2

are linear angles.
So,

∠ 1 + ∠ 2 = 180 °

⇒ ∠ 1 + 120 ° = 180 °

⇒ ∠ 1 = 180 ° − 120 °

⇒ ∠ 1 = 60 °

Apply property of corresponding angles in a transversal.

∠ 1 = 60 ° ∠ 2 = 60 °

That is,

∠ 1

and

∠ 2

are equal and they are the corresponding angles in

m

and

n

made by transversal

p

.
Since they are equal, lines

m

and

n

are parallel.
Given statement is true.
Hence, option 1 is correct.

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