Lines and Angles
Exercise 5.1
1). Find the complement of each of the following angles:
i) 200
ii). 630
iii). 570
Solution:
i) 200
let the complementary of 200 be x.
x + 20 = 90
x = 90 – 20
x = 70
ii). 630
let the complementary of 630 be x.
x + 63 = 90
x = 90 – 63
x = 27
iii). 570
let the complementary of 570 be x.
x + 57 = 90
x = 90 – 57
x = 33
2). Find the supplement of each of the following angles:
i) 1050
ii). 870
iii). 1540
Solution:
i) 1050
let the supplementary of 1050 be x.
x + 105 = 180
x = 180 – 105
x = 75
ii). 870
let the supplementary of 870 be x.
x + 87 = 180
x = 180 – 87
x = 93
iii). 1540
let the supplementary of 1540 be x.
x + 154 = 180
x = 180 – 154
x = 26
3). Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65º, 115º (ii) 63º, 27º (iii) 112º, 68º
(iv) 130º, 50º (v) 45º, 45º (vi) 80º, 10º
Solution:
(i) 65º, 115º
The Sum of the two angles is 65 + 115 = 180
The given pair of angles are supplementary.
(ii) 63º, 27º
The Sum of the two angles is 63 + 27 = 90
The given pair of angles are complementary.
(iii) 112º, 68º
The Sum of the two angles is 112 + 68 = 180
The given pair of angles are supplementary.
(iv) 130º, 50º
The Sum of the two angles is 130 + 50 = 180
The given pair of angles are supplementary.
(v) 45º, 45º
The Sum of the two angles is 45 + 45 = 90
The given pair of angles are complementary.
(vi) 80º, 10º
The Sum of the two angles is 80 + 10 = 90
The given pair of angles are complementary.
4). Find the angle which is equal to its complement.
The angle which is equal to its complement is 45.
5). Find the angle which is equal to its supplement.
The angle which is equal to its supplement is 90.
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?
In supplementary angle, the sum of angles is always equal to 180.
∠1 and ∠2 are supplementary angles.
If ∠1 is decreased, then ∠2 will increase so that the sum is always equal to 180.
7). Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?
Answer
(i) acute?
Two angles cannot be supplementary if both of them are acute.
(ii) obtuse?
Two angles cannot be supplementary if both of them are obtuse.
(iii) right?
Two angles are supplementary if both of them are right angles.
8). An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?
In complementary angles the sum of two angles is always equal to 90.
Therefore, if one angle is greater than 450 then the complement is less than 450.
9). In the adjoining figure:
(i) Is ∠1 adjacent to ∠2?
Yes.
(ii) Is ∠AOC adjacent to ∠AOE?
No.
(iii) Do ∠COE and ∠EOD form a linear pair?
Yes.
(iv) Are ∠BOD and ∠DOA supplementary?
Yes.
(v) Is ∠1 vertically opposite to ∠4?
Yes.
(vi) What is the vertically opposite angle of ∠5?
∠COB (∠2 + ∠3)
10). Indicate which pairs of angles are:
(i) Vertically opposite angles. (ii) Linear pairs.
Answer:
(i) Vertically opposite angles.
∠5 and ∠2 + ∠3
∠1 and ∠4
(ii) Linear pairs.
(∠5 and ∠4), (∠5 and ∠1), (∠1, ∠2 and ∠3), and (∠2, ∠3 and ∠4) are linear pairs.
11). In the following figure, is ∠1 adjacent to ∠2? Give reasons.
∠1 is not adjacent to ∠2 because they don’t have a common vertex.
12). Find the values of the angles x, y, and z in each of the following:
i). 550 and ∠x are vertically opposite angles
∠x = 550
550 and ∠y are forming linear pair
550 + ∠y = 180
∠y = 180 – 550
∠y = 1250
∠y and ∠z are vertically opposite angles
∠y = 1250
∠z = 1250
Ans: ∠x = 550
∠y = 1250
∠z = 1250
ii). 400 and ∠y are forming linear pair
400 + ∠y = 180
∠y = 180 – 40
∠y = 1400
∠z and ∠y are forming linear pair
∠z + ∠y = 180
∠z + 140 = 180
∠z = 180 – 140
∠z = 400
400, ∠x and ∠y are forming linear pair
40 + 40 + ∠y = 180
∠x + 80 = 180
∠x = 180 – 80
∠x = 1000
Ans: ∠x = 1000
∠y = 1400
∠z = 400
13). Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is 90.
(ii) If two angles are supplementary, then the sum of their measures is 180.
(iii) Two angles forming a linear pair are supplementary.
(iv) If two adjacent angles are supplementary, they form a linear pair.
(v) If two lines intersect at a point, then the vertically opposite angles are always equal.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are obtuse.
14). In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
(ii) Adjacent complementary angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair
Answer:
(i) Obtuse vertically opposite angles
∠AOD and ∠BOC
(ii) Adjacent complementary angles
∠AOE and ∠AOB
(iii) Equal supplementary angles
∠AOE and ∠EOD
(iv) Unequal supplementary angles
∠BOC and ∠COD
∠BOA and ∠AOD
(v) Adjacent angles that do not form a linear pair
∠AOE and ∠AOB
∠AOE and ∠EOC
∠DOE and ∠DOC
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