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.
Problem 1 :
An angle measures 38° less than its complement.
Solution :
The required angle be x.
If two angles are complementary to each other, then its sum will be 90 degree.
Required angle = 90 - 38
= 52
So, the required angle is 52 degree.
Problem 2 :
Find the measure of angle that is 10° more than its complement.
Solution :
The required angle be x.
If two angles are complementary to each other, then its sum will be 90 degree.
Required angle - Its complement = 10
x - (90 - x) = 10
x - 90 + x = 10
2x = 10 + 90
2x = 100
x = 50
= 52
So, the required angle is 52 degree.
Problem 3 :
Find the measure of an angle that is 30° less than its supplement.
Solution :
Let x be the required angle.
Its supplement will be 180 - x
(180 - x) - 30 = x
180 - x - 30 = x
150 - x = x
150 = x + x
2x = 150
x = 150/2
x = 75
So, the required angle is 75 degree.
Problem 4 :
The supplement of an angle is thirty more than twice the angle.
Solution :
Let x be the required angle.
Its supplement = 180 - x
180 - x = 2x + 30
180 - x - 2x = 30
180 - 3x = 30
180 - 30 = 3x
3x = 150
x = 150/3
x = 50
So, the required angles is 50.
Problem 5 :
An angle is one-third its supplement.
Solution :
Let x be the required angle
ITs supplement will be 180 - x
x = (1/3) of (180 - x)
x = (180 - x)/3
3x = 180 - x
3x + x = 180
4x = 180
x = 180 / 4
x = 45
Problem 6 :
Find the measure of an angle whose complement and supplement sum is 194 degrees.
Solution :
If x be the angle measure, its complement will be 90 - x and its supplement will be 180 - x
90 - x + 180 - x = 194
270 - 2x = 194
-2x = 194 - 270
-2x = -76
x = 76/2
x = 38
Problem 7 :
One of two supplementary angles is 35 degrees more than twice the other.
Solution :
Let x and 180 - x be the supplementary angles.
180 - x = 2x + 35
180 - 35 = 2x + x
145 = 3x
x = 145/3
x = 48.3
Problem 8 :
An angle is 30 less than half its complement.
Solution :
Let x be the angle and its complement will be 90 - x
x = (90 - x)/2 - 30
x = (90 - x - 60)/2
2x = 30 - x
2x + x = 30
3x = 30
x = 30/3
x = 10
So, the required angle is 10.
Problem 9 :
The supplement of an angle is twenty four degree less than five times the angle. Find the measure of each angle.
Solution :
Let x and 180 - x will be supplementary angle.
180 - x = 5x - 24
180 - x - 5x = -24
180 - 6x = -24
180 + 24 = 6x
6x = 204
x = 204/6
x = 34
Problem 10 :
Two complementary angles have measures in the ratio 1 : 5. Find the measure of the larger angle.
Solution :
Let x and 90 - x will be the complementary angles.
From the given ratio, x and 5x are the required angles.
x + 5x = 90
6x = 90
x = 90/6
x = 15
Applying the value of x, we get
x = 15, 5x = 5(15) ==> 75
So, the required larger angle measure is 75 degree.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM