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

Solution:

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

(i) Solve for ∠DGC

Given AB || DG and BC is a transversal.

Also, ∠ABC = 70° (Given)

Since, ∠ABC = ∠DGC (Corresponding angles)

Therefore, ∠DGC = 70° → (1)

ii) Solve for ∠DEF

Given BC || EF and DE is the transversal. 

Also, ∠DGC = 70° [from (1)]

Since, ∠DGC = ∠DEF (Corresponding angles)

Therefore, ∠DEF = 70°

☛ Check: Class 7 Maths NCERT Solutions Chapter 5

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

Summary:

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

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