Complementary angles :
Two angles are complementary, if the sum of their measures is equal to 90.
Supplementary angles :
Two angles are supplementary angles if the sum of their measures is equal to 180 degrees.
Find the values of unknowns :
Problem 1 :
Solution :
In the picture the above angles are linear pairs.
a + 37 = 180
a = 180 - 37
a = 143
Problem 2 :
Solution :
Since the angles a and 39 are complementary, sum of those angles will be 90°.
a + 39 = 90
a = 90 - 39
a = 51°
Problem 3 :
Solution :
In the picture the above angles are linear pairs.
a + a = 180
2a = 180
a = 180/2
a = 90
Problem 4 :
Solution :
From the picture, it is clear
90 + a + 40 = 180
130 + a = 180
a = 180 - 130
a = 50
Problem 5 :
Solution :
h and 2h are supplementary.
h + 2h = 180
3h = 180
Divide by 3, we get
h = 180/3
h = 60
Problem 6 :
Solution :
x + 30 and 2x + 15 are supplementary.
x + 30 + 2x + 15 = 180
3x + 45 = 180
Subtracting 45
3x = 180 - 45
3x = 135
Divide by 3
x = 135/3
x = 45
Problem 7 :
Solution :
2x + 5 and 15x are complementary.
2x + 5 + 15x = 90
17x + 5 = 90
Subtracting 5 on both sides.
17x = 90 - 5
17x = 85
Dividing by 17 on both sides.
x = 85/17
x = 5
Problem 8 :
Solution :
3b and 48 are complementary.
3b + 48 = 90
Subtracting 48 on both sides.
3b = 90 - 48
3b = 42
Dividing by 3, we get
b = 42/3
b = 14
Problem 9 :
Solution :
3x + 5 and 2x are supplementary.
3x + 5 + 2x = 180
5x + 5 = 180
Subtracting 5 on both sides.
5x = 180 - 5
5x = 175
Divide by 5 on both sides.
x = 175/5
x = 35
Problem 10 :
Solution :
2x - 34 and x + 100 are supplementary.
2x - 34 + x + 100 = 180
3x + 66 = 180
Subtracting 66 on both sides.
3x = 180 - 66
3x = 114
Dividing by 3 on both sides.
x = 114/3
x = 38
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM