Question

In the figure shown above, $\angle 1$ forms a linear pair with

• A. $\angle 3$ only
• B. $\angle 4$ only
• C. Both $\angle 3$ and $\angle 4$

Answer 1

The correct option is C Both $\angle 3$ and $\angle 4$


$\angle 1$ and $\angle 3$ are adjacent angles with $OA$ as a common arm and are formed by the intersection of the lines $AB\&CD$.
Also, $\angle 1+\angle 3={180}^{\circ }$
$\Rightarrow \angle 1$ and $\angle 3$ forms a linear pair.

Similarly, $\angle 1$ and $\angle 4$ are adjacent angles with $OC$ as a common arm and formed by the intersection of lines $AB\&CD$
Also, $\angle 1+\angle 4={180}^{\circ }$
$\Rightarrow \angle 1$ and $\angle 4$ forms a linear pair.

Therefore, $\angle 1$ forms a linear pair with both the angles, i.e., $\angle 3$ and $\angle 4$.