Question

In the figure $l\parallel m$ and $p$ is a transversal, find the value of $x$, giving necessary reasons.

Answer 1

Given: $l\parallel m$ and $p$ is the transversal.
When two parallel lines are cut by a transversal, the resulting corresponding angles are congruent.

Here, $5x$ and $2x+24$ are the corresponding angles.

$\Rightarrow 5x=2x+24$

$\Rightarrow 5x-2x=24$

$\Rightarrow 3x=24$

$\Rightarrow x=\frac{24}{3}$

$\Rightarrow x=8$