CLASS-7 CHAPTER 5 LINES AND ANGLES EXERCISE-5.2

 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:(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

(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 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

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)

CLASS-7 MATHS CHAPTER-5 LINES AND ANGLES EXERCISE-5.1

                                                                  EXERCISE 5.1 

 Question 1.Find the complement of each of the following angles:

Solution:
(i) Complement of 20° = 90° – 20° = 70°
(ii) Complement of 63° = 90° – 63° = 27°
(iii) Complement of 57° = 90° – 57° = 33°

 Question 2.Find the supplement of each of the following angles:

Solution:
(i) Supplement of 105° = 180° – 105° = 75°
(ii) Supplement of 87° = 180° – 87° = 93°
(iii) Supplement of 154° = 180° – 154° = 26°

Question 4.Find the angle which equal to its complement.

Solution:
Let the required angle be x°.
its complement = (90 – x)°
Now, re = 90 – x ⇒ x + x = 90
⇒ 2x = 90 ∴ x = 902 = 45°
Thus the required angles are 45

Question 7.Can two angles be supplementary if both of them are:
(i) acute?
(ii) obtuse?
(iii) right?
(ii) Since, acute angle < 90°
∴ Acute angle + acute angle < 90° + 90° < 180° Thus, the two acute angles cannot be supplementary angles. (ii) Since, obtuse angle > 90°
∴ Obtuse angle + obtuse angle > 90° + 90° > 180°
Thus, the two obtuse angles cannot be supplementary angles.
(iii) Since, right angle = 90°
∴ right angle + right angle = 90° + 90° = 180°
Thus, two right angles are supplementary angles

 Question 8. An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?
Solution:
Given angle is greater than 45°
Let the given angle be x°.
∴ x > 45
Complement of x° = 90° – x° < 45° [ ∵ x > 45°]
Thus the required angle is less than 45

Question 10.Indicate which pairs of angles are:

(i) Vertically opposite angles
(ii) Linear pairs
Solution:
(i) Vertically opposite angles are ∠1 and ∠4, ∠5 and (∠2 + ∠3)

(ii) Linear pairs are
∠1 and ∠5, ∠5 and ∠4

Question 11.In the following figure, is ∠1 adjacent to ∠2? Give reasons.
Solution:
No, ∠1 and∠2 are not adjacent angles.

Reasons:
(i) ∠1 + ∠2 ≠ 180°
(ii) They have no common vertex