Complementary Angles

Complementary angles : When two angles add up to 900.
Examples :

1) 20, 70 2) 30,60 3) 1,89 etc.

The complement of an angle of measure 30
0 is the angle of 60 0 . And the complement of angle of measure 60 0 is the angle of 30 0

Important Points :

1) If two angles are complement of each other, then each is an acute angle.

2) Two obtuse angles can not be complement of each other.

3) Two right angles cannot be complement of each other.

Examples :

1) If two angles are complement of each other and one of the angle is of measure 50.Find the measure of other angle.

Solution :
As we know that sum of two complementary-angles is 90
0 .

Let two angles be x and y such that x = 50
0

So x +y = 90
0

50 + y= 90

y = 90 – 50

y = 40
0
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2) Find the measure of an angle which is complement of itself.

Solution :
Let the measure of the angle be x
0 .

Its complement = x
0

Sum of the measures of an angle and its complement is 90
0 .

x + x = 90

2x = 90

∴ x = 90/2 = 45
0
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3) The two complementary angles are in the ratio of 2:3. Find the measures of each angle.

Solution :
Let the ratio be x
The two angles will be 2x and 3x.
As they are complementary-angles,
2x + 3x = 90
5x = 90
∴ x = 90/5 = 18
Each angle will be,
2x = 2(18) = 36
0
3x = 3(18) = 54
0

Basic Geometry

Point
Lines
Angles
Lines and Angles
Complementary angles
Supplementary angles
Vertically Opposite Angles
Linear Pair Angles