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

   

Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

GSEB Solutions Class 7 Maths 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 \(\parallel\) b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a \(\parallel\) b.
(iii) If ∠4 + ∠5 = 180°, then a \(\parallel\) b.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 1
Solution:
(i) If two parallel lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two given lines are intersected by a transversal such that interior alternate angles are equal, then the lines are parallel.
(iii) If two given lines are intersected by a transversal such that the sum of the interior angles on the same side of the transversal is 180°, then the lines are parallel.

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

Question 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.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 2
Solution:
(i) The pairs of corresponding angles are:
(∠1, ∠5); (∠2, ∠6); (∠3, ∠l) and (∠4, ∠8)

(ii) The pairs of alternate interior angles are:
(∠2, ∠8) and (∠3, ∠5)

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

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

Question 3.
In the adjoining figures p \(\parallel\) g. Find the unknown angles.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 3
Solution:
Since, ∠e + 125° = 180°
[linear pair]
∴ ∠e = 180° – 125°
i.e. ∠e = 55°
∴ ∠e = ∠f
[Vertically opposite angles ]
∴ ∠f = 55° [∴ ∠e = 55°]
Also, ∠a =∠e [Corresponding angles]
∴ ∠a = 55°
Again ∠b = 125°
[Alternate exterior angles]
Since, ∠b and ∠c form a linear pair,
∴ ∠b + ∠c = 180° or 125° + ∠c = 180° or ∠c = 180° – 125° = 55°
Now, ∠b and ∠d are vertically opposite angles.
∴ ∠d = ∠b = 125° [∴ ∠b = 125°]
Thus, the required measures are:
∠a = 55°, ∠b = 125°, ∠c = 55°
∠d = 125°, ∠c = 55°, ∠f = 55°

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

Question 4.
Find the value of x in each of the following figures if l || m.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 4
Solution:
(i) l || m and t is transversal.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 5
∴ Alternate angles are equal, i.e. ∠x = ∠p
But ∠p + 110° = 180° [Linear pair]
or ∠p = 180° – 110° = 70°
∴ ∠x = 70° [∵ ∠p = ∠x]
Thus, the required value of x is 70°.

(ii) ∵ l and m are parallel and a is a transversal, I m
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 6
∴ Corresponding angles are equal, i.e. ∠x = 100°
Thus, the required value of x is 100°.

Question 5.
In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find:
(i) ∠DGC (ii) ∠DEF
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 7
Solution:
We have AB || ED and BC || EF
(i) BC is a transversal,
∴ ∠DGC = ∠ABC [Corresponding angles]
But ∠ABC = 70°
∴ ∠DGC = 70°

(ii) ED is a transversal to BC || EF
∴ ∠DEF = ∠DGC [Corresponding angles]
But ∠DGC = 70°
∴ ∠DEF = 70°

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

Question 6.
In the given figures below, decide whether l is parallel to m.
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 8
Solution:
(i) ∵ 44° + 126° = 170°
But 170° ≠ 180°
i.e. the sum of the interior angles on the same side of the transversal is not 180°.
∴ l and m are not parallel.

(ii) GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 9
∵ n is a transversal to l and m and ∠p = 75° [Vertically opposite angles]
Also ∠p + 75° = 75° + 75°
= 150°
And 150° ≠ 180°
∴ l and m are not parallel.

(iii) GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 10
∴ ∠p + 123° = 180° [Linear pair]
∴ ∠p = 180° – 123°
= 57°
∴ ∠ p = 57°
i.e. corresponding angles are equal
∴ l and m are parallel.

(iv) ∵ ∠1 + ∠2 = 180° [Linear pair]
∴ ∠1 + 98° = 180°
or ∠1 = 180° – 98° = 82°
or ∠1 = 82°
Since ∠3 = 72°
∴ ∠1 ≠ ∠3
GSEB Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 11
i.e. the corresponding angles are not equal. Thus, l and m are not parallel.

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