Question

In Fig., AB || CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Answer 1

In the given figure, AB || CD and t is a transversal line.
Now, let:
$$\begin{gathered} \angle 1=3x \\ \angle 2=2x \end{gathered}$$
Thus, we have:
$$\begin{gathered} \angle 1+\angle 2=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \therefore 3x+2x=180° \\ \Rightarrow 5x=180° \\ \Rightarrow x=\frac{180°}{5}=36° \\ \mathrm{Thus}, \\ \angle 1=3\times 36°=108° \\ \angle 2=2\times 36°=72° \end{gathered}$$
Now,
$$\begin{gathered} \angle 1=\angle 5=108°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 1=\angle 3=108°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \\ \angle 5=\angle 7=108°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \\ \angle 2=\angle 6=72°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 4=\angle 2=72°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \\ \angle 8=\angle 6=72°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \end{gathered}$$