Question

A road crosses a railway line at an angle of $$30^o$$ as shown in Fig.
Find the values of $$a,\ b$$ and $$c$$.

Answer 1

In given figure, $$l$$ parallel to $$m$$ and $$q$$ is a transversal.
$$\therefore \angle 1 = 30^o$$ ......$$(1)$$ [corresponding angles]
Here, $$m$$ is a straight line.
$$\therefore \angle b +\angle 1=180^o$$ [Linear pair]
$$\Rightarrow \angle b=180^o - 30^o =150^o$$ by using equation $$1$$
Similarly, $$p$$ parallel to $$q$$ and $$m$$ is a transversal.
$$\therefore \angle 1 = \angle 3 =30^o$$ .... $$(2)$$ [Corresponding angles]
$$\angle a = \angle 3$$ [Vertically opposite angles]
$$\therefore \angle a =30^o$$ [using $$2$$]
In addition, $$p$$ parallel to $$q$$ and $$l$$ is a transversal.
$$\therefore \angle 2 =30^o$$ ... [Corresponding angles]
Here, $$l$$ is a straight line.
$$\therefore \angle c + \angle 2=180^o$$ [Linear pair]
$$\therefore 30^o + \angle 2=180^o$$ [by equation $$(2)$$]
$$\Rightarrow \angle c=180^o-30^o$$
$$\Rightarrow \angle c=150^o$$
Therefore,
$$\Rightarrow \angle a=30^o$$
$$\Rightarrow \angle b=150^o$$
$$\Rightarrow \angle c=150^o$$