Question

In the given figure, a || b and c || d. If $\angle 1={75}^{\circ }$, what is the measure of $\angle 3$?

• A. ${105}^{\circ }$
• B. ${150}^{\circ }$
• C. ${75}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A

${105}^{\circ }$

Given a || b and c || d and $\angle 1={75}^{\circ }$
Since, a || b,
$\angle 1=\angle 2={75}^{\circ }$ (corresponding angles are equal)

Also c || d,
$\Rightarrow \angle 2+\angle 3={180}^{\circ }\left[\text{sum of co-interior angles is 180}\right]$
$\therefore \angle 3={180}^{\circ }-{75}^{\circ }={105}^{\circ }$