RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 Textbook Exercise Questions and Answers.

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

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

(i) If a || b, then ∠1 = ∠5.
Answer:
Pair of corresponding angles are equal.

(ii) If ∠4 = ∠6, then a || b.
Answer:
Pair of alternate interior angles are equal.

(iii) If ∠4 + ∠5 = 180°, then a || b.
Answer:
Pair of interior angles on the same side of the transversal are supplementary.

Question 2.
In the adjoining figure, identify :

(i) the pairs of corresponding angles.
Answer:
Pairs of corresponding angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8.

(ii) the pairs of alternate interior angles.
Answer:
(ii) Pairs of alternate interior angles: ∠2 and ∠8, ∠3 and ∠5.

(iii) the pairs of interior angles on the same side of the transversal.
Answer:
Pairs of interior angles on the same side of the transversal: ∠3 and ∠8, ∠2 and ∠5.

(iv) the vertically opposite angles.
Answer:
Vertically opposite angles: ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8.

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

Answer:
∵ p || q, d and 125° are the pair of corresponding angles.
∴ d = 125°
∵ p || q, c and f are the pair of interior angles on the same side of the transversal.
∴ d + f = 180°
⇒ 125° + f = 180°
⇒ f = 180° - 125°
∴ f = 55°

∵ p || q, c and f are the pair of corresponding angles.
∴ c = f
∵ c = 55°

∵ Angles a and c are vertically opposite angles.
∴a = c
∴ a = 55°

∵ Angles b and d are vertically opposite angles.
∴ b = d
∴ b = 125°

∵ Angles e and f are vertically opposite angles.
∴ e = f
∴ e = 55°

Question 4.
Find the value of * in each of the following figures, if l || m:
(i)

Answer:
∵ l || m and vertically opposite angles of 110° and x are the pair of interior angles on the same side of the transversal.
∴ x + 110° = 180°
∴ x = 180° - 110° = 70°

(ii)

Answer:
∵ l || m and x and 100 are the pair of corresponding angles.
∴ x = 100°

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

Answer:
(i) ∵ Lines AB || ED, BC is the transversal, ∠DGC and 70° are pair of corresponding angles.
∴ ∠DGC = 70°

(ii) ∵ Lines BC || EF, DE is the transversal ∠DEF and ∠DGC are pair of corresponding angles.
∴ ∠DEF = ∠DGC = 70°

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

Answer:
∵ Sum of pair of interior angles on the same side of the transversal = 126° + 44* = 170°
i.e. they are not supplementary.
∴ Lines l and m are not parallel.

(ii)

Answer:
∵ 75° and 180° - 75° = 105° are the pair of corresponding angles and they are not equal.
∴ Lines l and m are not parallel.

(iii)

Answer:
∵ 57° and 180° -123° = 57° are the pair of corresponding angles and they are equal. 
∴ Lines l and m are parallel.

(iv)

Answer:
∵ 72° and 180° - 98° = 82° are the pair of corresponding angles and they are not equal.
∴ Lines l and m are not parallel.