NCERT Solutions for Class 7 Maths - Chapter 5 Lines and Angles- Exercise 5.2

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Please find the detailed Solutions for class 7th Maths Chapter 5 – Lines and Angles Exercise 5.2 Solutions, you can check all the solutions from here chapter wise

NCERT Class 7th Mathematics Solutions – Detailed Chapter Wise

1. State the property that is used in each of the
following statements?

(i) If a || b, then ∠1 = ∠5.

Ans: Corresponding angle property

(ii) If ∠4 = ∠6, then a || b.

Ans: Alternate interior angle property

(iii) If ∠4 + ∠5 = 180°, then a || b.

Ans: Interior angles on the same side of the transversal are supplementary

2. In the adjoining figure, identify

(i) the pairs of corresponding angles.

Ans: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

(ii) the pairs of alternate interior angles.

Ans: ∠2 and ∠8, ∠3 and ∠5

(iii) the pairs of interior angles on the same
side of the transversal.

Ans: ∠2 and ∠5, ∠3 and∠8

(iv) the vertically opposite angles.

Ans: ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8

3. In the adjoining figure, p || q. Find the unknown
angles.

Sol: ∠d = 125° ( Corresponding Angles)

∠b= ∠d = 125° (vertically opposite angles)

∠d + ∠f = 180 °(Interior angles on the same side of the transversal are supplementary)

∠f = 180°-125°

∠f = 55°

∠e = ∠f (vertically opposite angles)

∠e = 55°

∠a = ∠e = 55° ( Corresponding Angles)

∠c= ∠a = 125° (vertically opposite angles)

4. Find the value of x in each of the following figures if l || m.

(i) y = 110°

y+x = 180° (linear pair)

x = 180°-110°

x = 70°

(ii) x+2x = 180° (Interior angles on the same side of the transversal are supplementary)

3x = 180°

3x/3 = 180°/3

x = 60°

(iii) x = 100° (corresponding angles)

5. In the given figure, the arms of two angles are parallel.
If ∠ABC = 70º, then find

(i) ∠DGC

Sol: Let AB and DE are two parallel lines and BC is the transversal

Then ∠ABC = ∠DGC ( Corresponding Angles)

∠DGC = 70°

(ii) ∠DEF

Sol: EF and BC are two parallel lines and DG is a transversal

Then ∠DGC = ∠DEF ( Corresponding Angles)

∠DEF = 70°

6. In the given figures below, decide whether l is parallel to m.

Sol:

(i) If l is parallel to m then Sum of Interior angles on same side of transversal should be equal to 180°

126°+ 44° = 170°

So l is not parallel to m

(ii) l is not parallel to m because corresponding angles are not equal.

(iii) 123° + x° = 180° (Linear pair)

x = 180° – 123° = 57°

Now, corresponding angles are equal. So l is parallel to m.

(iv) 98° + x = 180° (Linear pair)

x = 180° -98°

x = 82°

Since corresponding angles are not equal. So l is not parallel to m.

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