Question

In the figure, $p$ is transverse to lines m and n, $\angle 1={60}^o$ and $\angle 2=\frac{2}{3}$ of a right angle. Prove that $m\parallel n$.

Answer 1

Given: $\angle 1={60}^o$ and

$\angle 2=\frac{2}{3}$ of a right angle $=\frac{2}{3}\times {90}^o={60}^o$
$\angle 3=\angle 2$ ....... (vertically opposite angles)
$\Rightarrow \angle 3={60}^o$
Since, $\angle 1=\angle 3$
So, corresponding angles are equal then $m\parallel n$.