Question

In the adjoining figure, two lines $AC$ and $BD$ intersect at the point $O$. Which of the following are linear pairs? Check all that apply.

• A. $\angle 1$ and $\angle 2$
• B. $\angle 1$ and $\angle 3$
• C. $\angle 1$ and $\angle 4$
• D. $\angle 3$ and $\angle 4$

Answer 1

Answer: (A), (C), (D)

$\angle 3$ and $\angle 4$

$\underset{–}{\text{Linear Pair:}}$
Pair of adjacent angles whose non-common sides form a straight line and their measures add up to ${180}^o$.

The given figure is,
We will check all the options one by one.

(a.) $\angle 1$ and $\angle 2$
$\angle 1$ and $\angle 2$ share a common side $OB$ and their non-common sides $OA$ and $OC$ form the straight line $AC$.
$\therefore$ $\angle 1$ and $\angle 2$ form a linear pair.

(b.) $\angle 1$ and $\angle 3$
$\angle 1$ and $\angle 3$ don't share any common side.
$\therefore$ $\angle 1$ and $\angle 3$ don't form a linear pair.

(c.) $\angle 1$ and $\angle 4$
$\angle 1$ and $\angle 4$ share a common side $OA$ and their non-common sides $OB$ and $OD$ form the straight line $BD$.
$\therefore$ $\angle 1$ and $\angle 4$ form a linear pair.

(d.) $\angle 3$ and $\angle 4$
$\angle 3$ and $\angle 4$ share a common side $OD$ and their non-common sides $OA$ and $OC$ form the straight line $AC$.
$\therefore$ $\angle 3$ and $\angle 4$ form a linear pair.

So, options(a.), (c.) and (d.) are correct.