Question

In the adjoining figure , $ p\parallel q $ . Find the unknown angles.

Answer 1

Hint: It is better to understand the different properties of geometry. The angles can be found by using properties of parallel lines and straight lines.

Complete step-by-step answer:
Observe the diagram

Sum of the angles which form a linear pair is equal to $ {180^0} $
Therefore, from the diagram, we can say that
 $ 125^\circ + \angle e = 180^\circ $ (Linear pair)
So, we get
 $ \angle e = 180^\circ - 125^\circ $
 $ \Rightarrow \angle e = 55^\circ $
 $ \angle e = \angle f $ (Vertically opposite angles)
 $ \Rightarrow \angle f = 55^\circ $
 $ \angle a = \angle e $ (Corresponding angles of two parallel lines)
 $ \therefore \angle a = \angle e = 55^\circ $
 $ \Rightarrow \angle a = 55^\circ $
 $ \angle d = 125^\circ $ (Corresponding angles of two parallel lines)
 $ \angle a = \angle c $ (Vertically opposite angles)
 $ \Rightarrow \angle c = {55^0} $
 $ \angle b = \angle d $ (Vertically opposite angles)
 $ \Rightarrow \angle b = {125^0} $

Note: Such a question cannot be solved using what is given in the question. You need to figure out additional points to solve the problem using the given information. This question only can be solved if you know the properties of adjoining figures.