1. Complementary and Supplementary angles

2. Complementary Angle
Two angles are complementary if and only if the sum of their angle is 90.
Example 1: Check if the pair of angle given below is complementary
50° H
40° Q P S
Solution
Given : PHQ=40 , QHS = 50
Step1:- Find the sum of pair of angles
PHQ + QHS = = 90
Step2:- Check if the sum of pair of angles is 90
If the sum is 90 then the angles are complementary else it is not complementary
∴ Sum of pair of angles is 90, hence PHQ and QHS are complementary

3. Example 2: Find whether the pair of angle below are complementary angles
Angle pair
Sum of the angle
Equal to 90
Complementary 20
and 50 20
+ 50 = 70 no no
60 and 30
= 90
yes
yes 40
and 40 40
+ 40 = 80 no no
55 and 25
=90
yes
yes
120 and 60
= 180 no no 13
and 67 13
+ 67 = 90
yes
yes

4. Example 3: Find the complementary angle of 35
Solution
We know that two angles are complementary if and only if the sum of their angle is 90.
∴ To find the complement, subtract the given angle from 90
90 – 35 = 55
Ans: The complementary angle of 35 is 55.

5. Example 4: Find the complementary angle of given angle-
Complementary
angle
Complementary angle
= 90
given angle
Angle 45 90 – 45 45 30 90 – 30 60 20 90 – 20 70 10 90 – 10 80 70 90 – 70 20 60 90 – 60 30

6. Supplementary Angle
Two angles are supplementary if and only if the sum of their angle is 180.
Example1: Check if the pair of angle given below is supplementary
Solution
Given : PHQ=130 , QHS = 50
50° H
130° Q P S
Step1:- Find the sum of pair of angles
PHQ + QHS = = 180
Step2:- Check if the sum of pair of angles is 180
If the sum is 180 then the angles are supplementary else it is not supplementary
∴ Sum of pair of angles is 90, hence PHQ and QHS are supplementary

7. Example 2: Find whether the pair of angle below are supplementary angles
Angle pair
Sum of the angle
Equal to 180
Supplementary
110 and 50
= 160 no no
160 and 20
= 180
yes
yes
70 and 140
= 210 no no
135 and 45
=180
yes
yes
40 and 50
= 90 no no
145 and 35
= 180
yes
yes

8. Example 3: Find the supplementary angle of 130
Solution
We know that two angles are supplementary if and only if the sum of their angle is 180.
∴ To find the complement, subtract the given angle from 180
180 – 130 = 50
Ans: The supplementary angle of 130 is 55.

9. Example 5: Find the Complementary and Supplementary angle of given angle-
Supplementary
angle
Supplementary angle
= 180
given angle
Angle
100
180 -
100 80 60
180 - 60
120
120
180 -
120 60 30
180 - 30
150 90
180 - 90 90
140
180 -
140 40

10. Example 2: Find whether the pair of angle below are supplementary angles90 -
Complementary angle =
given angle
Supplementary angle = 90 -
given angle
Angle 35 – 90
35 = 55 –
180
35 = 145
Given angle >90, so no
complementary angle possible
120 –
180
120 = 60 70 – 90
70 = 20 –
180
70 = 110 80 – 90
80 = 10 –
180
80 = 100
Given angle >90, so no
complementary angle possible
150 –
180
150 = 30 20 – 90
20 = 70 –
180
20 = 60

11. Try these
1. Find the supplement angle of 112°?
2. Find the complement angle of 63°?