Question

In the given figure, line l intersects two parallel lines PQ and RS. Then which one of the following is not true?

• A. $\angle 6=\angle 7$
• B. $\angle 1=\angle 3$
• C. $\angle 4=\angle 7$
• D. $\angle 2=\angle 4$

Answer 1

The correct option is C $\angle 4=\angle 7$

Form the given figure, $PQ||RS$ and $l$ is transversal therefore,
$\angle 1=\angle 3\left[\text{corresponding angles}\right]\angle 2=\angle 4\left[\text{corresponding angles}\right]$
Also, $\angle 5=\angle 6\left[\text{vertically opposite angles}\right].....\left(i\right)$
and $\angle 5=\angle 7\left[\text{corresponding angles}\right].....\left(ii\right)\Rightarrow \angle 6=\angle 7[\text{from Eqs. (i) and (ii)}$
As we can see that option a, b and c are correct. So d is our required option which is not true.
Also, We can see that $\angle 2=\angle 4$ and $\angle 2+\angle 7={180}^{\circ }$ because 2 and 7 are linear pair.
$\Rightarrow \angle 4+\angle 7={180}^{\circ }$ and if option d will be correct then $\angle 4=\angle 7={90}^{\circ }$ must hold.