# Complementary Angles

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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 300 is the angle of 600. And the complement of angle of measure 600 is the angle of 300

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 900.

Let two angles be x and y such that x = 500

So x +y = 900

50 + y= 90

y = 90 – 50

y = 400
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2) Find the measure of an angle which is complement of itself.

Solution :
Let the measure of the angle be x0.

Its complement = x0

Sum of the measures of an angle and its complement is 900.

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) = 360
3x = 3(18) = 540

Basic Geometry

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