Question

In the given figure, AB$||$CD, $\angle 1:\angle 2=3:2$. Then $\angle 6$ is __________.

• A. ${72}^o$
• B. ${36}^o$
• C. ${108}^o$
• D. ${144}^o$

Answer 1

The correct option is A ${72}^o$

Angles $1$ and $2$ are supplementary angles.

$\therefore \angle 1+\angle 2={180}^o$

and $\angle 1=\frac{3}{2}\angle 2$ ( as given in the question )

We get, $\frac{5}{2}\angle 2={180}^o\Rightarrow \angle 2={72}^o$

From the figure,

$\because AB||CD$

$\therefore \angle 6=\angle 2\Rightarrow \angle 6={72}^o$