Question

In Fig., line l || m, ∠1 = 120° and ∠2 = 100°, find out ∠3 and ∠4.

Answer 1

In the given figure, ∠1 = 120° and ∠2 =100°.
Since l || m, so
$$\begin{gathered} \angle 2=\angle 5=100°\left(\mathrm{Alternate}\mathrm{interior}\mathrm{angles}\right) \\ \angle 5+\angle 3=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \Rightarrow \angle 3=180°-\angle 5=180°-100°=80° \end{gathered}$$
Also,
$$\begin{gathered} \angle 1+\angle 6=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \Rightarrow \angle 6=180°-\angle 1=180°-120°=60° \end{gathered}$$
We know that the sum of all the angles of triangle is 180°.
$$\begin{gathered} \therefore \angle 6+\angle 3+\angle 4=180° \\ \Rightarrow 60°+80°+\angle 4=180° \\ \Rightarrow 140°+\angle 4=180° \\ \Rightarrow \angle 4=180°-140°=40° \end{gathered}$$