NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

NCERT Solutions Class 7 Mathematics
Chapter – 5 (Lines and Angles)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 5 Lines and Angles Exercise 5.2 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 5 Lines and Angles

• NCERT Solution Class 7 Maths Exercise – 5.1

Exercise – 5.2

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^o, then a || b.

Solution –

(i) If a || b, then ∠1 = ∠5.
Corresponding angles property is used in the above statement.

(ii) If ∠4 = ∠6, then a || b.
Alternate interior angles property is used in the above statement.

(iii) If ∠4 + ∠5 = 180^o, then a || b.
Interior angles on the same side of transversal are supplementary.

2. In the adjoining 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) The vertically opposite angles.

Solution –

(i) The pairs of corresponding angles.
The pair of corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7.

(ii) The pairs of alternate interior angles.
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.
The pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8.

(iv) The vertically opposite angles.
The vertically opposite angles are ∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8

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

Solution –
∠d = ∠125^o  —————– [∵ corresponding angles]
We know that, Linear pair is the sum of adjacent angles is 180^o
⇒ ∠e + 125^o = 180^o —————– [Linear pair]
⇒ ∠e = 180^o – 125^o
⇒ ∠e = 55^o
From the rule of vertically opposite angles,
∠f = ∠e = 55^o
∠b = ∠d = 125^o
By the property of corresponding angles,
∠c = ∠f = 55^o
∠a = ∠e = 55^o

4. Find the value of x in each of the following figures if l || m.
(i)        (ii)

Solution –

(i) Let the angle opposite to 110° be y.
∴ y = 110° (Vertically opposite angles)
⇒ ∠x + ∠y = 180° (Sum of interior angle on the same side of transversal)
⇒ ∠x + 110° = 180° .
∴ ∠x = 180° – 110° = 70°
Thus x = 70°

(ii) ∠x = 110° (Pair of corresponding angles)

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

Solution –

(i) ∠DGC
Let us consider that AB || DE
BC is the transversal line intersecting AB and DG
By the property of corresponding angles,
∠DGC = ∠ABC
Then,
∠DGC = 70^o

(ii) ∠DEF
Let us consider that BC || EF
DE is the transversal line intersecting BC and EF
By the property of corresponding angles,
∠DEF = ∠DGC
Then,
∠DEF = 70^o

6. In the given figures below, decide whether l is parallel to m.
(i)                                 (ii)

(iii)                                  (iv)

Solution –

(i) Sum of interior angles on the same side of transversal
⇒ 126° + 44° = 170° ≠ 180°
∴ l is not parallel to m.

(ii) Let angle opposite to 75° be x.
x = 75° [Vertically opposite angles]
∴ Sum of interior angles on the same side of transversal
⇒ x + 75° = 75° + 75°
⇒ 150° ≠ 180°
∴ l is not parallel to m.

(iii) Let the angle opposite to 57° be y.
∴ ∠y = 57° (Vertically opposite angles)
∴ Sum of interior angles on the same side of transversal
⇒ 57° + 123° = 180°
∴ l is parallel to m.

(iv) Let angle opposite to 72° be z.
∴ z = 70° (Vertically opposite angle)
Sum of interior angles on the same side of transversal
⇒ z + 98° = 72° + 98°
⇒ 170° ≠ 180°
∴ l is not parallel to m.