Question

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

Answer 1

It is given that $\angle 1:\angle 2=3:2$. So, let
$\angle 1=3x°$ and $\angle 2=2x°$
But $\angle 1$ and $\angle 2$ from a linear pair.
$\therefore \angle 1+\angle 2=180°$
$\Rightarrow 3x°+2x°=180°\Rightarrow 5x°=180°$
$\Rightarrow x=\frac{180°}{5}=36°$
$\therefore \angle 1=3x°=(3\times 36)°=108°$
and, $\angle 2=2x°=(2\times 36°)=72°$
Now, $\angle 1=\angle 3$ and $\angle 2=\angle 4$ [Vertically opposite angles]
$\therefore \angle 4=72°$ and $\angle 3=108°$
Now, $\angle 6=\angle 2$ and $\angle 3=\angle 7$ [Corresponding angles]
$\Rightarrow \angle 6=72°$ and $\angle 7=108°[\angle 2=72°]$
[Vertically opposite angles]
Again, $\angle 5=\angle 7$ and $\angle 8=\angle 6$
$\therefore \angle 5=108°$ and $\angle 8=72°$
Hence, $\angle 1=108°,\angle 2=72°,\angle 3=108°,\angle 4=72°,\angle 5=108°,\angle 6=72°,\angle 7=108°$ and $\angle 8=72°$