Chapter 5 Lines and Angles Exercise 5.2
Question 1.
State the property that is used in each of the following statements?
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-8.png)
(i) If a || b, then ∠1 = ∠5
(ii) If ∠4 = ∠6, then a || b
(iii) If ∠4 + ∠5 = 180°, then a || b
Solution:
(i) Given a || b
∴ ∠1 = ∠5 (Pair of corresponding angles)
(ii) Given: ∠4 = ∠6
∴ a || b [If pair of alternate angles are equal, then the lines are parallel]
(iii) Given: ∠4 + ∠5 = 180°
∴ a || b [If sum of interior angles is 180°, then the lines are parallel]
Question 2.
In the given figure, identify
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-9.png)
(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.
Solution:
(i) 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 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.
Question 3.
In the given figure, p || q. Find the unknown angles.
Solution:
∠e + 125° = 180° (Linear pair)
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-10.png)
∴ ∠e = 180° – 125° = 55°
∠e = ∠f (Vertically opposite angles)
∴ ∠f= 55°
∠a = ∠f= 55° (Alternate interior angles)
∠c = ∠a = 55° (Vertically opposite angles)
∠d = 125° (Corresponding angles)
∠b = ∠d = 125° (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:
(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)
Question 5.
In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find
(i) ∠DGC
(ii) ∠DEF
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-11.png)
Solution:
Given
AB || DE
BC || EF
∠ABC = 70°
∠DGC = ∠ABC
(i) ∠DGC = 70° (Pair of corresponding angles)
∠DEF = ∠DGC
(ii) ∠DEF = 70° (Pair of corresponding angles)
Question 6.
In the given figure below, decide whether l is parallel to m.
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-12.png)
![](https://rajboardexam.in/wp-content/uploads/2022/07/image-13.png)
Solution:
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.
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