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Complementary angles

 

 
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Complementary angles
 
 
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A pair of angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
s are complementary if the sum of their measures is 90 degrees
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
.

If the two complementary angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a right angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
.

In Euclidean geometry
Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Greek mathematics Euclid of Alexandria. Euclid's Elements is the earliest known systematic discussion of geometry....
, the two acute angles
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.

The adjective complementary is from Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
 complementum, associated with the verb complere, "to fill up".






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Complementary Angles
A pair of angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
s are complementary if the sum of their measures is 90 degrees
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
.

If the two complementary angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a right angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
.

In Euclidean geometry
Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Greek mathematics Euclid of Alexandria. Euclid's Elements is the earliest known systematic discussion of geometry....
, the two acute angles
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.

The adjective complementary is from Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
 complementum, associated with the verb complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.

See also

  • Supplementary angles
    Supplementary angles

    A pair of angles is supplementary if their measures add up to 180 degree s.If the two supplementary angles are adjacent angles , their non-shared sides form a straight line ....
  • Triangle
    Triangle

    A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
    s


External links

  • - Interactive applet and explanation of the characteristics of complementary angles.