# Ex.5.2 Q3 Lines and Angles - NCERT Maths Class 7

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## Question

In the adjoining figure, p || q. Find the unknown angles ## Text Solution

Reasoning:

First, by using linear pair find the measure of $$\angle e$$ and then find the corresponding and vertically opposite angle to $$\angle e$$ and again by using linear pair find the value of $$\angle b$$ and its vertically opposite angle.

Steps:

Given $$p || q$$ and it is intersected by a transversal.

$$\angle = 125^\circ$$ (Corresponding angle)

Since, $$125^\circ$$ $$+ \angle e = 180^\circ$$ (Linear pair)

$$\angle e = 180^\circ - 125^\circ$$

$$\angle e = 55^\circ$$

$$\angle e = \angle f = 55^\circ$$ (Vertically opposite angles)

$$\angle e = \angle a = 55^\circ$$ (Corresponding angles)

$$\angle a + \angle b = 180^\circ$$ (Linear pair)

$$55^\circ + \angle b = 180^\circ$$

$$\angle b = 180^\circ - 55^\circ$$

$$\angle b =125^\circ$$

Also$$, \angle b = \angle d = 125^\circ$$ (Vertically opposite angles)

$$\angle a = \angle c = 55^\circ$$ (Vertically opposite angles)

Thus$$, \angle a = 55^\circ; \angle b = 125^\circ; \angle c = 55^\circ; \angle d = 125^\circ;$$

$$\angle e = 55^\circ ; \angle f = 55^\circ$$

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