Angle Definition

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The shape formed by two lines, around their common points also called the vertex. Angles are measured in degrees.

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The two arms are known as the side of an angle. The common point is known as the vertex. 

Properties of Angles

Important properties of the angle are:

  • For one side of a straight line, the sum of all the angles always measures 180 degrees.

  • The sum of all angles always measures 360 degrees around a point.

  • An angle is a figure where, from a common position, two rays appear. The vertex of the angle is called this point and its arms or sides are called the two rays forming the angle.

  • A reflex angle is called an angle which is greater than 180 degrees but less than 360 degrees.

  • They form a linear pair of angles if two opposite angles add up to 180 degrees. 

  • The two opposite pairs of angles formed are called vertically opposed angles where two lines parallel each other. 

Types of Angles

There are six types of angles commonly known in geometry:

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  1. Acute Angles: When the measurement of an angle is between 0 to 90 degrees. 

  2. Obtuse Angles: The opposite of an acute angle is an obtuse angle. It is the angle that lies between 90 degrees and 180 degrees; the obtuse angle is greater than 90 degrees and less than 180 degrees.

  3. Right Angles:  A right angle is equal to 90 degrees. Any angle of fewer than 90 degrees is an acute angle, and an obtuse angle is an angle greater than 90 degrees.

  4. Straight Angles: A straight angle is 180 degrees when measured.

  5. Reflex Angles: A reflex angle is any angle that has a measure that is greater than 180 degrees but less than 360 degrees (coinciding with 0 degrees).

  6. Full Rotation: Complete rotation, or full angle, is considered an angle equal to 360 degrees. When one of the arms takes a full rotation to form an angle, it is made.

Angle Types Based on Rotation

Angles can be of 2 types based on the direction of rotation:

  • Positive Angles

  • Negative Angles

Positive Angles

Positive angles are the angles determined from the base in the counterclockwise direction. Positive angles are often used to show geometry angles. From the origin, if an angle is drawn in the (+x, +y) plane, it forms a positive angle.

Negative Angles

Negative angles are the angles determined from the base in a clockwise direction. From the origin, if an angle is drawn towards the (x, -y) plane, it forms a negative angle.

Pair of Angles

By combining two angles, we can create different types of angles, such as:

  • Complementary angles:  If the sum of the two angles is 180°, they are called complementary angles. 

  • Supplementary angles: If the sum of the two angles is 90°, they are called supplementary angles.

  • Linear Pair: If the non-common arms of adjacent angles are exactly opposite each other or extend in the other direction, then they are called linear pairs. By linear, it is clear that they form a straight line.

  • Adjacent angles: If two angles are attached to a common arm and have a common vertex, so they are considered adjacent angles, and the non-common arms are on either side of the common arm, too. 

  • Vertically Opposite Angles: The angle created on either side of the common vertex is called vertical angles or vertically opposite angles if both lines converge at a single point (called the vertex).

Fun facts

  1. The term "angle" came from the Latin word Angulus, which means "a little bending."

  2. Eudemus, who defined an angle as a deviation from a straight line, first used the concept of angle.

FAQ (Frequently Asked Questions)

1. What is Meant By Interior and Exterior Angles?

The angle formed on the inside of a circle is considered as the internal angle, while the exterior angle is the angle formed on the outside of the shape.

2. What are the Six Different Angles in Geometry Based on Measurement?

Six different angles based on magnitude are:

Acute angle, Obtuse angle, Right angle, Straight angle, Reflex angle, and full angle.

3. Find the Unknown Angle x for the Given Triangle ABC, where ∠A = 25° and ∠B = 92°?

Given that ∠A = 25° and ∠B = 92°;

Let ∠C = x

We know that the sum of interior angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180°

25°+ 92° + x = 180°

117° + x = 180°

x = 180° – 117°

x = 63°

Therefore, the value of the unknown angle is 63°.