Angle Definition

Geometry is a branch of mathematics that deals with the study of shapes and their measurements. It also focuses on the relative configuration of the shapes and its spatial properties. We know that geometry is classified into 2D Geometry and 3D Geometry. Before dividing that, all the geometrical shapes are formed by points, lines, rays and plane surface. When the two lines or the rays converge at a common point, the measurement between the two lines is called an “Angle”. In this article, let’s discuss the angle definition and its types in detail.

Angle Definition in Maths

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex. The angle that lies in the plane does not have to be in the Euclidean space. In case if the angles are formed by the intersection of two planes in the Euclidean or the other space, the angles are considered as dihedral angles. The angle is generally represented using the Greek letter θ, α, β etc.

Types of Angles

The angles are classified under the following types:

  • Acute Angle – an angle measure less than 90 degrees
  • Right Angle – an angle is exactly at 90 degrees
  • Obtuse Angle – an angle whose measure is greater than 90 degrees and less than 180 degrees
  • Straight Angle – an angle which is exactly at 180 degrees
  • Reflex Angle – an angle whose measure is greater than 180 degrees and less than 360 degrees
  • Full Angle – an angle whose measure is exactly at 360 degrees

Different Types of Angles

Based on these angles and the lines, it is further classified into different types such as complementary angles, supplementary angles, adjacent angles, vertical angles, alternate interior angles, alternate exterior angles and so on.

Angle Example

Question:

Find the unknown angle x for the given triangle ABC, where ∠A = 28° and ∠B = 91°

Solution:

Given that ∠A = 28° and ∠B = 91°

Let ∠C = x

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

Therefore,

∠A + ∠B + ∠C = 180°

28°+ 91° + x = 180°

119° + x = 180°

x = 180° – 119°

x = 61°

Therefore, the value of unknown angle is 61°

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