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# Formulas for Finding Angle Measures

## Introduction

Angle is a property which are widely used in the mathematics.In geometry, an angle is the figure formed by two lines, having a common endpoint, called the vertex of the angle and where as in trignometry they are used as a value. Angle can be calculated using the magnitudes of these two lines.The magnitude of the angle is the "amount of rotation" that separates the two lines, and can be measured by considering the length of circular arc.

Usually angles are defined using the unit degree and radians depending upon the value given to the angle.Radian is the angle subtended by an arc of a circle that has the same length as the circle's radius.Degrees may be further divided into minutes and seconds, Each degree is divided into 60 equal parts called minutes.

Example: Five and a half degrees is usually written 5.5°.Based on the above theory the degrees are further defined as below, five and a half degrees can be called 5 degrees and 30 minutes, written 5° 30'.

## Properties

Angle of 90 degrees is called Right angle.

Angle smaller than right angle are called Acute angle.

Angle larger than right angle and smaller than 180 degrees are called Obtuse angle.

Angles between 180 and 360 degrees are called reflex angles.

If the sum of two angles is 360 degrees then the two angles are called as Explementary angles.

## General form

Angle is generally represented with symbol "?".

In order to measure an angle ?,The length of the arc s is then divided by the radius of the circle r, and possibly multiplied by a scaling constant k.

Formula: ?= s(k)
r

## Concepts of angles in geomentry

Angle is most important in geomentry. The concepts of equality, sums, and differences of angles are important and used throughout geomentry.These are mainly used in constructing the geomentric constructions.

## Interior angle

The sum of measures of interior angle of a polygon with "n" sides is

Formula: (n-2)x180 degress.

## Example:

For triangle the sum of interior angles is

(3-2)x180=180 degrees

Since triangle has 3 sides ,n=3.

And the measure of single interior angle of a polygon with "n" sides can be calculated using :

Formula: (n-2)x180
n

## Example:

The measure of an interior angle of a regular pentagon which has 5 sides can be calculated as

(5-2)x180 =108 degress.
5

## Exterior angle

The angle supplementary to the interior angle is called the exterior angle,sum of exterior angle of a polygon will be 360 degrees.If the interior angle exceeds 180 degrees the exterior angle will be negative.

## Concept of angles in trignomentry

A Euclidean angle is completely determined by the corresponding right triangle in trignomentry. If ? is a Euclidean angle then:

cos?=$\fracx\sqrtx^2+y^2$

sin?=$\fracy\sqrtx^2+y^2$