Question

In the figure, AB || CD and $\angle 1:\angle 2=3:2$. The measure of $\angle 8$ is ${72}^{\circ }$ .

• A. True
• B. False

Answer 1

The correct option is A

True

Let $\angle 1=3x$ and $\angle 2=2x$
Now $\angle 1+\angle 2={180}^{\circ }$ (Linear pair)
$\Rightarrow 3x+2x={180}^{\circ }$
$\Rightarrow 5x={180}^{\circ }\Rightarrow x={36}^{\circ }$
$\angle 2=2x=2\times {36}^{\circ }={72}^{\circ }$

Since AB || CD, we have
$\angle 6=\angle 2={72}^{\circ }$ (corresponding angles)

$\angle 8=\angle 6={72}^{\circ }$ (vertically opposite angle)

Hence, the statement is true.