Question

In which condition the co-interior angles of two parallel lines will be same in measure?

• A. They cannot be same as the co-interior angle theorem states that the sum of the measure of the angles is ${180}^o$.
• B. The transversal line is perpendicular to parallel lines.
• C. They are always same in measure.

Answer 1

The correct option is B The transversal line is perpendicular to parallel lines.

Let the co-interior angles of two parallel lines is same in measure, i.e., $\angle a$ and $\angle a.$

The co-interior angle theorem states that the sum of the measure of the angles is ${180}^o$.
$\Rightarrow \angle a+\angle a={180}^o$
$\Rightarrow 2\angle a={180}^o$
$\Rightarrow \angle a=\frac{{180}^o}{2}={90}^o$

$\therefore$ The transversal should make a right angle with the parallel lines.

This special case is depicted in the following figure:

Hence, the above assumption is possible.