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Angle, Types of Angles

Contents

Angle:

An angle is a figure formed by two rays with the same initial point. The common initial point is called the vertex of the angle and the rays forming the angle are called its arms or sides.

O is the vertex and rays OA and OB are the arms of the angle. Each arm defines a particular direction in the plane of the angle. The arms are often joined by a small circular arc near the vertex.

Naming an angle:

In order to identify the angles, when there are more than one in the same plane, we name the angles.
In order to name a given angle formed by two rays with the same initial point, we name the vertex and name one more point on each arm.

Geometry_angle

Point B is called the vertex of the angle.
Point A lies on the ray BA.
Point C lies on the ray BC.

The angle is named as angle ABC or angle CBA.
It is written as \(\angle{ABC} or \angle{CBA}\). The \(\angle\) stands for the angle.
Sometimes, we name an angle by writing the letter at the vertex of the angle. For example, \(\angle{ABC}\) is also denoted as \(\angle{B}\) or angle B.

An angle is also named by placing a number (1, 2, 3, etc.)or a small letter (a, b, c etc.) near the small circular arc connecting the two arms of the angle.

Geometry_Angle1Geometry_Angle2

Reference Angle Calculator tool helps in finding a reference angle for degrees and radians.

Angle as rotation of a Ray:

Geometry_Angle3
Let there be a ray with initial point O. Suppose it starts rotating in the plane from the initial position OA about the point O until it reaches the final position OB.
Then, we say that an angle \(\angle{AOB}\) has been described by the rotating ray with O as vertex and its arms as OA and OB.

Magnitude of an Angle:

The magnitude of an angle is the amount of rotation through which one of the arms must be rotated about the vertex to bring it to the position of the other arm.

Measuring an angle:

geometry_measuring an angle

Let us measure \(\angle{ABC}\).
The unit for measuring an angle is degree (written as °). An angle is measured by a protractor.
A protractor has markings from 0° to 180° from both the ends, so that angles on both the sides can be measured.
For measuring an angle, place the baseline of the protractor on one arm of the angle such the midpoint of the baseline coincides with the vertex of the angle. Start measuring from 0. The degree measure shown by the other arm is the measure of the angle.
Observe that the measure of \(\angle{ABC}\) = 60°.
It is written as m\(\angle{ABC}\) = 60°.

Types of Angles:

Right Angle:
Geometry_right angle

An angle whose measure is 90°, is called a right angle.
m\(\angle{JKL}\) = 90°
So, \(\angle{JKL}\) is a right angle.

Acute Angle:

Geometry_acute angle

An angle whose measure is less than 90°, is called an acute angle.
m\(\angle{XYZ}\) < 90°
So, \(\angle{XYZ}\) is an acute angle.

Obtuse Angle:

Ggeometry_obtuse angle
An angle whose measure is more than 90°, is called an obtuse angle.
m\(\angle{ABC}\) > 90°
So, \(\angle{ABC}\) is an obtuse angle.

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