Question

In the figure given below, l and m are two parallel lines. Which of the following statement is true?

• A. $\angle$1 + $\angle$8 = 180${}^{\circ }$
• B. $\angle$7 + $\angle$8 + $\angle$5= 180${}^{\circ }$
• C. $\angle$1 + $\angle$2 + $\angle$4 = 180${}^{\circ }$
• D. $\angle$3 + $\angle$5 + $\angle$6 = 180${}^{\circ }$

Answer 1

The correct option is A $\angle$1 + $\angle$8 = 180${}^{\circ }$

From Euclid's 5th postulate, 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."
$\Rightarrow$ If the lines are parallel, the sum of those two angles is 180${}^{\circ }$.

$\therefore$ $\angle$1 + $\angle$8 = 180${}^{\circ }$ and $\angle$3 + $\angle$6 = 180${}^{\circ }$