Question

IN the figure l||m and n is a ttansversal such that $\angle 3:\angle 8=1:2.$ Find $\angle 4$ and $\angle 3$.

Answer 1

In the given figure $\angle 8=\angle 6$ (vertically opposite angles)

It is given that $\angle 3:\angle 8=1:2$

Therefore $\angle 3:\angle 6=1:2$

And $\angle 3+\angle 6={180}^o$ (co-interior angle)

Now let the constant be $x$

Then,$1x+2x=180$

$\Rightarrow x={60}^o$

Therefore $\angle 3={60}^o$

And $\angle 4={180}^o-{60}^o={120}^o$ (linear pair)