# Ex.5.2 Q5 Lines and Angles - NCERT Maths Class 7

## Question

In the given figure, the arms of two angles are parallel. If \(\angle ABC = 70^\circ,\) then find:

(i) \(\angle DGC\)

(ii) \(\angle DEF\)

## Text Solution

**Reasoning:**

Let’s visually model this problem. There is one operation that can be done. According to this model, the resultant value of corresponding angle will be equal to \(\angle DGC.\)

Now, it’s a matter of finding measure of \(\angle DGC.\)

**Steps:**

(i) Solve for \(\angle DGC\)

Given \(AB || DG\) and \(BC\) is transversal

Also,

\(\angle ABC = 70^\circ\text{ (Given)}\)

Since,

\(\angle ABC = \angle DGC\text{(Corresponding angles)}\)

Therefore\(, \angle DGC = 70^\circ→(1)\)

**Reasoning:**

Let’s visually model this problem . There is one operation that can be done.According to this model, the resultant value of corresponding angle will be equal to \(\angle DGC.\) Now, it’s a matter of finding measure of \(\angle DEF.\)

**Steps:**

(ii) Solve for \(\angle DEF\)

Given \(BC || EF\) and \(DE\) is transversal

Also, \(\angle DGC = 70^\circ \text{(from 1)}\)

Since,

\(\angle DGC = \angle DEF \text{(Corresponding angles)}\)

Therefore\(, \angle DEF = 70^\circ\)