In the given figure, if lines AB and CD meet each other when extended towards A or C, then the relation between $∠ 1 and ∠ 2$ is .

(∠1 +∠2) = 180°

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(∠1 +∠2) < 180°

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(∠1 +∠2) > 180°

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Solution

The correct option is B (∠1 +∠2) < 180°
According to Euclid's postulates,
"If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles. "
So, in the above figure the lines AB and CD meet each other when extended towards A or C if $∠ 1 + ∠ 2 < 180^{\circ}$ .

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