Question

For two lines, what happens when the interior angles on the same side of the transversal add up to a value less than 180${}^{\circ }$?

• A. They never meet.
• B. They meet on the side on which the sum of the angles is less than 180${}^{\circ }$.
• C. They meet on the side opposite to the side on which the sum of the angles is less than two right angles.
• D. They meet at two points.

Answer 1

The correct option is B They meet on the side on which the sum of the angles is less than 180${}^{\circ }$.

From Euclid's postulates, we know
"If a straight line falling on two straight lines makes the interior angles on the same side of it taken together is less than two right angles, then the two straight lines, if produced infinitely, meet on that side on which the sum of the angles is less than two right angles"

From the above figure, we can see that $\angle$PAB and $\angle$RBA add up to a value less than 180${}^{\circ }$.
It can be observed that the two lines meet at a point on the same side when extended.