Question

In the given figure, lines $PQ$ and $RS$ intersect at point $O$. If $\angle 1={53}^o$, find all other angles.

Answer 1

Since $PQ$ and $RS$ are two lines intersecting each other, thus

$\angle 1=\angle 3\left(\text{Vertically opposite angle}\right)$

$\angle 2=\angle 4\left(\text{Vertically opposite angle}\right)$

Now,

$\angle 1=53°=\angle 3$

Also,

$\angle 1+\angle 2=180°\left(\text{Linear pair of angles}\right)$

$\Rightarrow \angle 2=180°-53°=127°$

$\therefore \angle 4=\angle 2=127°$