Question

In the figure, AB || CD and $\angle 1:\angle 2=3:2$. The measure of $\angle 6$ is

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

Answer 1

The correct option is A ${72}^{\circ }$

Let $\angle 1=3x$ and $\angle 2=2x$
Now $\angle 1+\angle 2={180}^{\circ }$ (Linear pair)
$\Rightarrow 3x+2x={180}^{\circ }$
$\Rightarrow 5x={180}^{\circ }\Rightarrow x={36}^{\circ }$
$\angle 2=2x=2\times {36}^{\circ }$
Since AB || CD, we have
$\angle 6=\angle 2={72}^{\circ }$ (corresponding angles)