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 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

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Basic Geometry

• Point
• Lines
• Angles
• Lines and Angles
• Complementary angles
• Supplementary angles
• Vertically Opposite Angles
• Linear Pair Angles
• Adjacent Angles
• Parallel Lines
• Solved Problems on Intersecting Lines
• Solved Problems on Parallel Lines

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