Chapter 5 Lines and Angles Ex 5.1 Solutions
Question - 1 : - Find the complement of each of the following angles:
Answer - 1 : -
(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:
Answer - 2 : -
(i) Supplement of 105° = 180° – 105° = 75°
(ii) Supplement of 87° = 180° – 87° = 93°
(iii) Supplement of 154° = 180° – 154° = 26°
Question - 3 : - Identify which of the following pairs of angles are complementary and which are supplementary?
(i) 65°, 115°
(ii) 63°, 27°
(iii) 112°, 68°
(iv) 130°, 50°
(v) 45°, 45°
(vi) 80°, 10°
Answer - 3 : -
(i) 65° (+) 115° = 180°
They are supplementary angles.
(ii) 63° (+) 27° = 90°
They are complementary angles.
(iii) 112° (+) 68° = 180°
They are supplementary angles.
(iv) 130° (+) 50° = 180°
They are supplementary angles.
(v) 45° (+) 45° = 90°
They are complementary angles.
(vi) 80° (+) 10° = 90°
They are complementary angles.
Question - 4 : - Find the angle which equal to its complement.
Answer - 4 : -
Let the required angle be x°.
its complement = (90 – x)°
Now, re = 90 – x ⇒ x + x = 90
⇒ 2x = 90 ∴ x = 90/2 = 45°
Thus the required angles are 45°.
Question - 5 : - Find the angle which is equal to its supplement.
Answer - 5 : -
Let the required angle be x°.
∴ it supplement = (180 – x)°
Now, x = 180 – x
⇒ x + x = 180
⇒ 2x = 180°
∴ x=180/2=90∘
Thus, the required angle is 90°.
Question - 6 : - In the given figure, ∠1 and ∠2 are supplementary angles.
If ∠1 is decreased, what changes should take place in∠2 so that both the angles still remain supplementary.
Answer - 6 : -
∠1 + ∠2 = 180° (given)
If ∠1 is decreased by some degrees, then ∠2 will also be increased by the same degree so that the two angles still remain supplementary.
Question - 7 : - Can two angles be supplementary if both of them are:
(i) acute?
(ii) obtuse?
(iii) right?
Answer - 7 : - 
Question - 8 : - An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?
Answer - 8 : -
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 - 9 : - In the following figure:
(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite angle to ∠4?
(vi) What is the vertically opposite angle of ∠5?
Answer - 9 : -
(i) Yes, ∠1 and ∠2 are adjacent angles.
(ii) No, ∠AOC is not adjacent to ∠AOE. [ ∵ OC and OE do not lie on either side of common arm OA] .
(iii) Yes, ∠COE and ∠EOD form a linear pair of angles.
(iv) Yes, ∠BOD and ∠DOA are supplementary. [∵ ∠BOD + ∠DOA = 180°]
(v) Yes, ∠1 is vertically opposite to ∠4.
(vi) Vertically opposite angle of ∠5 is ∠2 + ∠3 i.e. ∠BOC.
Question - 10 : - Indicate which pairs of angles are:
(i) Vertically opposite angles
(ii) Linear pairs
Answer - 10 : -
(i) Vertically opposite angles are ∠1 and ∠4, ∠5 and (∠2 + ∠3)
(ii) Linear pairs are
∠1 and ∠5, ∠5 and ∠4