Question

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?

Answer 1

Let us assume that the lines meet in the opposite side of the given interior angles.

Angle sum property of a triangle = 180 degrees.

Since the lines can't meet without forming a triangle it is impossible to have them meet.

Because the sum of two angles is already greater than 180 degrees.

There fore ,

The lines will extend to meet at side of the interior angles.