Question

In figure, $m\parallel n$ and angles $1$ and $2$ are in the ratio $3:2$. Determine all the angles from $1$ to $8$.

Answer 1

Let $\angle 1=3x$ and $\angle 2=2x$.

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

or, $5x={180}^o$

or, $x={36}^o$.

$\therefore \angle 1={108}^o$ and $\angle 2={72}^o$.

Since $m\parallel n$ and $l$ is the intersector, then

$\angle 3=\angle 1={108}^o$ and $\angle 4=\angle 2={72}^o$ [Opposite angles]

and $\angle 7=\angle 5=\angle 2={72}^o$.

If $\angle 5={72}^o$ then $\angle 6={108}^o=\angle 8$.