Angles

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An angle can be defined as two rays sharing a common vertex.

[edit] Measurement of angles

An angle is measured by considering the ratio of an arc to the radius of the arc. A scaling constant k is multiplied for various units.

\theta=\frac{s}{r}(k)

°=== Units of measurement === There are various units of measurement for measuring angles, however the most commonly used are degrees or radians.

  • Degrees - It is denoted by a small circle as a superscript (°). One full rotation is considered equal to 360 degrees. Degree is subdivided into minutes and seconds as:-

1° = 60' (60 minutes) = 60" (60 seconds)

  • Radians - This is a number and is dimensionless. A full circle is equal to (pronounced two pi) radians. This in conjunction with the formula for arc length defines the historically famous irrational number π (pronounced pi ) as,
\pi=\frac{1}{2}\frac{circumference~of~a~circle}{radius~of~the~circle}
There are four types of angles: Acute, obtuse, straight, and right. Pi is also equal to 3.1 An Acute angle is less then 90°. An Obtuse angle is more than 90°. A straight angle is 180°. A right angle is 90°.