# In the given figure, the arms of two angles are parallel

If ∠ABC = 70º, then find (i) ∠DGC (ii) ∠DEF

**Solution:**

We use the geometry concepts like parallel lines, supplementary angles, vertically opposite angles and adjacent angles to solve the problem.

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 ∠DGC. Now, it’s a matter of finding measure ∠DGC.

(i) Solve for ∠DGC

Given AB || DG and BC is transversal. Also, ∠ABC = 70° (Given)

Since, ∠ABC = ∠DGC (Corresponding angles)

Therefore, ∠DGC = 70° → (1)

ii) Solve for ∠DEF

Given BC || EF and DE is transversal. Also, ∠DGC = 70° (from (1))

Since, ∠DGC = ∠DEF(Corresponding angles)

Therefore, ∠DEF = 70°

**Video Solution:**

## In the given figure, the arms of two angles are parallel. If ∠ABC = 70º, then find: (i) ∠DGC (ii) ∠DEF

### NCERT Solutions for Class 7 Maths - Chapter 5 Exercise 5.2 Question 5

In the given figure, the arms of two angles are parallel. If ∠ABC = 70º, then find (i) ∠DGC (ii) ∠DEF

(i) ∠DGC = 70°; (ii) ∠DEF = 70°.