Question

In the given figure $l,m$ and $n$ are parallel lines, and the lines $p$ and $q$ are also parallel find the values of $a,b$ and $c$.

Answer 1

Since, lines $l,n$ are parallel and $q$ is transversal.
Therefore, $6a={120}^{\circ }$ as they are corresponding angles.
$\Rightarrow a=\frac{{120}^{\circ }}{6}$
$\therefore a={20}^{\circ }$
Also, lines $p,q$ are parallel and $n$ is transversal.
Therefore,$4c={120}^{\circ }$ as they are corresponding angles
$\Rightarrow c=\frac{{120}^{\circ }}{4}$
$\therefore c={30}^{\circ }$
Again, lines $m,n$ are parallel and $p$ is transversal,
Therefore $4c=3b$ as they are corresponding angles
$\Rightarrow b=\frac{4c}{3}$
$\Rightarrow b=\frac{4\times {30}^{\circ }}{3}$
$\therefore b={40}^{\circ }$