# Angles

An angle is the space, measured in degrees, between two intersecting lines or surfaces.

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Angle:

Two rays with common initial point or end point forms an angle. The common end point is called the vertex of the angle.

The two rays are called the arms or sides of the angle.

Two line segments with a common end point forms an angle. The common end point is called the vertex of the angle.

The two line segments are called the arms or sides of the angle.

Naming an angle:

A point each, on both the sides and the vertex are mentioned to name any angle. The angle below may be named as angle ABC or as angle CBA.

We use the symbol  '' to denote the word 'angle'. We use only capital letters to name any angle and the vertex point is always given in the middle.

We also name an angle by writing a number inside the angle.

Measuring an angle:

We compare the size of the given angle with a unit angle, while measuring it.

Unit angle: Draw two opposite rays with the same initial point.

The angle so formed is called a straight angle. We divide this into 180 equal parts and each subdivision is called a unit angle. The measure (size) of each unit angle is a "degree". Symbol used for a degree is "o". For example, 3 degrees is written as 3o and 180 degrees is written as 180o.

PROTRACTOR:

To find the number of degrees in an angle, we use a protractor.

A straight angle is divided into 180 equal subdivisions on a protractor, marked from 0 to 180. You find two scales marked 0 to 180, one in clockwise direction and the other in anti-clockwise direction. Each subdivision stands for 1°.

Steps to measure:

1. Place the center of the protractor on the vertex of the angle.
2. Base line should fall along any of the sides.
3. The scale (clock wise or anti-clock wise direction), which begins with zero on the side, is chosen.
4. Read the mark on the scale where the other arm crosses it.

Example:

Measure of angle ABC = 60o.

Types of Angles:

Based on the size, angles are classified as acute, right and obtuse angles.

Acute Angle: Angle measuring between 0 and 90 degrees is called an acute angle.

Example:

The following angles are all acute angles.

Right Angle: Angle measuring 90 degrees is called a right angle. Two rays or line segments or lines that meet at a right angle are said to be perpendicular.

Example:

The following angles are both right angles.

Obtuse Angle:

Angle measuring between 90 and180 degrees is called an obtuse angle.

Example:

The following angles are all obtuse.