## Lines and Angles NCERT Solution for Class 7 Maths Chapter 5 Exercise 5.2

**Question 1:- State the property that is used in each of the following statements?**

**(i) If a || b, then ∠1 = ∠5**

**(ii) If ∠4 = ∠6, then a || b**

**(iii) If ∠4 + ∠5 = 180°, then a || b**

**Solution 1:-**

(i) Given, a || b

**Corresponding Angle Property:-** If two parallel lines a and b are cut by a transversal line then each pair of corresponding angles be equal in measure.

By the property of corresponding angles :- ∠1 = ∠5

(ii) Given, ∠4 = ∠6

**Alternative Interior Angles Property:- **If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal.

When a transversal line cuts two lines such that pairs of alternate interior angles are equal than the line have to be parallel.

So, a || b [ If pair of alternate angles are equal, then the lines are parallel ]

(iii) Given: ∠4 + ∠5 = 180°

**Co-interior Angle Property:- **Interior angles on the same side of the transversal are supplementary.

When transversal line cuts two lines such that pairs of interior angles on the same side of the transversal are supplementary then the line have to be parallel.

So, a || b [ If sum of interior angles is 180°, then the lines are parallel ]

**Question 2 :- In the given figure, identify**

**(i) the pairs of corresponding angles.**

**(ii) the pairs of alternate interior angles.**

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

**(iv) Vertical opposite angle.**

**Solution 2:-**

(i) The pair of corresponding angles are :-

∠1 and ∠5;

∠2 and ∠6;

∠3 and ∠7;

∠4 and ∠8.

(ii) The pairs of alternate interior angles are :-

∠2 and ∠8;

∠3 and ∠5.

(iii) The pairs of interior angles on the same side of the transversal are :-

∠2 and ∠5;

∠3 and ∠8.

(iv) The vertically opposite angle are :-

∠1 and ∠3;

∠2 and ∠4;

∠5 and ∠7;

∠6 and ∠8.

**Question 3:- In the given figure, p || q. Find the unknown angles.**

**Solution 3:- **Given, p || q and cut by transversal line

∠e + 125° = 180° [ By the property of Linear pair ]

So, ∠e = 180° – 125° = 55°

∠e = ∠f [ By the property of Vertically opposite angles ]

So, ∠f= 55°

∠a = ∠f= 55° [ By the property of Alternate interior angles ]

∠c = ∠a = 55° [ By the property of Vertically opposite angles ]

∠d = 125° [ By the property of Corresponding angles ]

∠b = ∠d = 125° [ By the property of Vertically opposite angles ]

Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125°, ∠e = 55°, ∠f= 55°.

**Question 4 :- Find the value of x in each of the following figures if l || m**

**Solution 4:- **

(i) Given l || m and t is transversal line

Let the angle opposite to 110° be y.

So, y = 110° [ By the property of Vertically opposite angles ]

∠x + ∠y = 180° [ By the property of supplementary angle ]

∠x + 110° = 180° .

∴ ∠x = 180° – 110° = 70°

Thus x= 70°

(ii) Given l || m and a || b

∠x = 110° [ By the property of corresponding angles ]

**Question 5 :- In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find**

**(i) ∠DGC**

**(ii) ∠DEF**

**Solution 5:-**

(i) Given, AB || DE and BC || EF

∠ABC = 70° and BC transversal line

∠DGC = ∠ABC = 70 [ By the property of corresponding angle ]

(ii) Given, AB || DE and BC || EF

∠ABC = 70° and DE transversal line

∠DEF = 70° [ By the property of corresponding angle ]

**Question 6 :- In the given figure below, decide whether l is parallel to m.**

**Solution 6:-**

Sum of interior angles on the same side of transversal

126° + 44° = 170° ≠ 180°.

So, the line L is not parallel to the line M because sum of interior angle should be 180°.

(ii) Let angle opposite to 75° be x.

x = 75° [By the property of Vertically opposite angles]

Since, the sum of interior angles on the same side of transversal =

x + 75° = 75° + 75°

= 150° ≠ 180°

So, the line L is not parallel to the line M because sum of interior angle should be 180°.

(iii) Let the angle opposite to 57° be y.

So the angle ∠y = 57° [ By the property of Vertically opposite angles ]

Since, the sum of interior angles on the same side of transversal

= 57° + 123° = 180°

Hence, the line L is parallel to the line M.

(iv) Let angle opposite to 72° be z.

∴ z = 70° (Vertically opposite angle)

Since the sum of interior angles on the same side of transversal

= z + 98° = 72° + 98°

= 170° ≠ 180°.

So, the line L is not parallel to the line M because sum of interior angle should be 180°.