Question

In the given figure, l || m and a transversal t cuts them. If ∠1 = 120°, find the measure of each of the remaining marked angles.

Answer 1

We have, $\angle 1=120°$. Then,
$$\begin{gathered} \angle 1=\angle 5\left[\text{Corresponding angles}\right] \\ \Rightarrow \angle 5=120° \\ \angle 1=\angle 3\left[\text{Vertically-opposite angles}\right] \\ \Rightarrow \angle 3=120° \end{gathered}$$

$$\begin{gathered} \angle 5=\angle 7\left[\text{Vertically-opposite angles}\right] \\ \Rightarrow \angle 7=120° \\ \angle 1+\angle 2=180°\left[\text{Since AFB is a straight line}\right] \\ \Rightarrow 120°+\angle 2=180° \end{gathered}$$

$$\begin{gathered} \Rightarrow \angle 2=60° \\ \angle 2=\angle 4\left[\text{Vertically-opposite angles}\right] \\ \Rightarrow \angle 4=60° \\ \angle 2=\angle 6\left[\text{Corresponding angles}\right] \end{gathered}$$

$$\begin{gathered} \Rightarrow \angle 6=60° \\ \angle 6=\angle 8\left[\text{Vertically-opposite angles}\right] \\ \Rightarrow \angle 8=60° \\ \therefore \angle 1=120°\mathbf{,}\mathbf{}\angle 2=60°,\angle 3=120°,\angle 4=60°,\angle 5=120°, \\ \angle 6=60°,\angle 7=120°\text{and}\angle 8=60° \end{gathered}$$