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Q.

State true or false.

If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is $120 ∘$ , then the two straight lines, if produced indefinitely. meet on the side on which the sum of angles is less than $120 ∘$ .

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a

True

b

False

answer is A.

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Detailed Solution

Given three straight lines and sum of interior angles on the same side =

120 ∘

.

Question Image

From the above figure, lines AB and CD cannot meet with each other because the sum of base angles is exceeding the limit of 180°.
So, the line will be able to meet on the side of AE and CF because the sum of the base angles is equal to 120° which is

x + y = 120 °

and less than 180°.
The meeting side of the straight lines will be on that side which provides sum of its angles as

120 ∘

or <

120 ∘

.
Therefore, the statement is true.
Hence, option (1) is correct.

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State true or false.If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 120 ∘ , then the two straight lines, if produced indefinitely. meet on the side on which the sum of angles is less than 120 ∘ .