Question

Question 37

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

(a)$\angle 1=\angle 3$
(b) $\angle 2=\angle 4$
(c) $\angle 6=\angle 7$
(d) $\angle 4=\angle 7$

Answer 1

Form the given figure, PQ||RS and l is transversal therefore,
$\angle 1=\angle 3\left[\text{corresponding angles}\right]\angle 2=\angle 4\left[\text{corresponding angles}\right].....\left(i\right)$
Also, $\angle 5=\angle 6\left[\text{vertically opposite angles}\right].....\left(ii\right)$
and $\angle 5=\angle 7\left[\text{corresponding angles}\right].....\left(iii\right)\Rightarrow \angle 6=\angle 7[\text{from Eqs. (ii) and (iii)}$
Also, $\angle 2+\angle 8={180}^{\circ }\left[\text{linear pair}\right]\Rightarrow \angle 4+\angle 8={180}^{\circ }[\angle 2=\angle 4]$