Types of angles

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The types of angles are those categories in which the arcs that are formed from the intersection of two lines and whose measurement is normally in degrees or radians can be classified.

Different criteria can be used to classify the types of angles, as we will see below.

Types of angles according to their measure

According to their measure, the angles can be classified as follows:

  • Sharp: Measures less than 90º or π / 2 radians.

  • Blunt: Measures more than 90º or π / 2 radians, but less than 180º or π radians.
  • Straight: It measures 90º or π / 2 radians.
  • Flat: It measures 180º or π radians.
  • Oblique or concave: It is greater than 180º or π radians and less than 360º or 2π radians (It should be noted that a convex angle is one that measures less than 180º).
  • Complete or perigonal: Measure 360º or 2π radians

Types of angle according to their position with respect to another

Depending on how one is located with respect to another, the angles can be:

  • Consecutive: They are located next to each other. Formally explained, they share the same vertex. In the image below, α and β are consecutive angles.
  • Adjacent: They are located on the same line, so they form a flat angle. That is, they add up to 180º, like α and β in the following graph:
  • Opposed by the vertex: They are those that share the same vertex and one is formed by the prolongation of the sides that make up the other angle. In the lower image, α and δ are vertically opposed as are β and γ.

Types of angles according to the result of their summation

Depending on the result of their summation, the angles can be:

  • Complementary: Their sum is equal to 90º.
  • Supplementary: They add up to 180º.

In the image below, α and β are complementary, while δ and ε are supplementary.

Types of angles according to their location on a circle

The types of angles, depending on their location on a circle, are:

  • Central: It is one where the sides that form it are two radii of the circumference, a radius being that segment that joins the center of the figure with any point on it. In the image below, a central angle would be α.
  • Inscribed: As is the case of β in the example below, an inscribed angle is one whose vertex is a point on the circumference and is formed by two lines intersecting the circumference. That is, they cut the figure at two points.
  • Semi-inscribed: Its vertex is within the circumference and is formed by two sides, one is secant to the circumference, but the other is tangent to it. That is, it does not cut the figure, but only touches it at one point. Such an angle is γ in the lower image.
  • Exterior: Its vertex is outside the circumference, and its sides can be tangent or secant to the figure. In the image below, δ is an exterior angle.

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