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,
$\angle 1=\angle 3\left[correspondingangles\right]\angle 2=\angle 4\left[correspondingangles\right].....\left(i\right)$
Also, $\angle 5=\angle 6\left[verticallyoppositeangles\right].....\left(ii\right)$
and $\angle 5=\angle 7\left[correspondingangles\right].....\left(iii\right)\Rightarrow \angle 6=\angle 7[fromEqs.(ii\left)and\right(iii)$
Also, $\angle 2+\angle 8={180}^{\circ }\left[linearpair\right]\Rightarrow \angle 4+\angle 8={180}^{\circ }[\angle 2=\angle 4]$