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

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## 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$$, \angle ABC = 70^\circ$$ (Given)

Since$$, \angle ABC = \angle DGC$$ (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$$, \angle DGC = 70^\circ$$ (from 1)

Since$$, \angle DGC = \angle DEF$$ (Corresponding angles)

Therefore$$, \angle DEF = 70^\circ$$

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