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

## 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.

\(\angle = 125^\circ\\ \text{(Corresponding angle)}\)

Since,

\(125^\circ+ \angle e = 180^\circ \\ \text{(Linear pair)}\)

\(\angle e = 180^\circ - 125^\circ\)

\(\angle e = 55^\circ\)

\(\angle e = \angle f = 55^\circ \\ \text{(Vertically opposite angles)}\)

\(\angle e = \angle a = 55^\circ \\ \text{(Corresponding angles)}\)

\(\angle a + \angle b = 180^\circ \\ \text{ (Linear pair)}\)

\(55^\circ + \angle b = 180^\circ\)

\(\angle b = 180^\circ - 55^\circ\)

\(\angle b =125^\circ\)

Also,

\(\angle b = \angle d = 125^\circ \\ \text{(Vertically opposite angles)}\)

\(\angle a = \angle c = 55^\circ \\ \text{(Vertically opposite angles)}\)

Thus,

\(\angle a = 55^\circ; \angle b = 125^\circ; \angle c = 55^\circ;\)

\( \angle d = 125^\circ;\angle e = 55^\circ ; \angle f = 55^\circ\)