Question

If a transversal passes through two parallel lines, then the interior angles on the same side of the transversal add up to:

• A. 90${}^{\circ }$
• B. 180${}^{\circ }$
• C. 120${}^{\circ }$
• D. 360${}^{\circ }$

Answer 1

The correct option is B 180${}^{\circ }$

Euclid's fifth postulate states that:
"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"


Conversely, if the sum is equal to 180${}^{\circ }$, the two lines never meet. Or in other words, the lines are parallel.