Angles: Types and Categories of Angles

len Alfred Ajibola - Mon, 15th July, 2019 @ 10:37

Topics in Mathematics

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Academic Questions in Mathematics

Please check out our Test Your Knowledge page to see all Questions and Answers

Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____.

  • A. oblique
  • B. curved
  • C. vertical
  • D. perpendicular
  • E. parallel
  • F. horizontal

The two sides that forms an angle are referred to as the _____.

  • A. arms
  • B. vertexes
  • C. bays
  • D. zones
  • E. limbs
  • F. dune

The point where the two sides of an angle meet is termed the _____.

  • A. arms
  • B. vertex
  • C. bays
  • D. zones
  • E. limbs 
  • F. dune

How many digits are there in -223.00

  • A. 1
  • B. 2
  • C. 3
  • D. 4
  • E. 5
  • F. 6

30% of 2 is equal to _____.

  • A. 30
  • B. 0.6
  • C. 75
  • D. 0.25
  • E. 0.3
  • F. 60

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What are Angles?

Angles, triangles, squares, circles, cubes, cones and cylinders are all part of geometry in mathematics.

Geometry is the branch of mathematics that deals with the study of shapes, sizes and dimensions of a variety of things.

As a mathematics student, understanding angles is very important because it’s vital in building, constructions and designs.

Sailors use angles to navigate their path along the sea while a carpenter can apply them to make beautiful designs of his job.

Amazingly, sport men and women can utilize angles in making an excellent performance. For instance, the use of angles can be applied in taking throws in basket ball while a footballer can actually use it to curl a free-kick into the football net.

By definition, an angle is a figure formed by two sides sharing a common endpoint.

For instance, an angle is formed where two walls in the corner of our homes meet OR at the point where the two arms of a scissors meet.

Note: The two sides that forms the angle are called Arms or Rays while the endpoint where both sides meet is called the Vertex.

The figure below illustrates this:

Arms and Vertex of Angles - Len Academy

Note: The angle formed will depend on the amount of turn between each arm.

Angle - Len Academy

  • Most times, an angle is represented by the figure .
  • The angle in the above figure can be represented as ABC.
  • The unit of an angle is in degree (that is, angles are measured in degrees and a protractor can be used to achieve this).
  • Please read on Trigonometry (Sine, Cosine and Tangent) here.

Labeling of Angles

Angles can be labeled mainly in two ways

1. By using the three letters on the shape of the specific angle

Importantly, the angle is formed on the middle letter; which is its vertex.

In tha above diagram, the angle will be labeled as ABC

2. By giving the angle a name:

The name are often denoted with a Greek letter like α (alpha) or θ (theta). Also, we can also name the angle with a lowercase letters like p or q.

Still using the above diagram as a basis, the angle will be labeled as α


Categories of Angles

An angle can be categorized as either interior or exterior based on where they are formed with regards to a shape.

Categories of Angles - Len Academy

  • Interior angles are formed inside a shape. In the above diagram, the angle is formed inside a pentagon. (A pentagon has 5 sides and 5 angles).

  • Exterior angles are formed outside a shape via a line extending from the adjoining sides.
    Please read on the Type of Lines in Mathematics here.


Types/Names of Angles

The type and name of an angle can be determined based on it’s measurement.

If we increased the size of the angle to a certain degree, the name of the angle changes automatically.

For instance, an angle less than 90o is named as an acute angle but as soon as we increase the size of the angle to 90o, its name changes to a right angle.

The photo below shows the various types and names of Angles:

Types and Names of Angles - Len Academy

  1. Acute Angle: An angle that is less than 90o

  2. Right Angle: An angle that is exactly 90o

  3. Obtuse Angle: An angle that is greater than 90o but less than 180o

  4. Straight Angle or Angle on a Straight Line: An angle that is exactly 180o

  5. Reflex Angle: An angle that is greater than 180o but less than 360o

  6. Complete Angle or Full Rotation Angle: An angle that is exactly 360o

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Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.

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Amazing facts in Mathematics

31,556,926 seconds makes one year


From 0 to 1000, the only number that has the letter “a” in it is “one thousand”.


The division symbol "÷" is actually called an obelus


Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself. 


40 is spelt as FORTY and not FOURTY. It is the only number that is spelt with letters arranged in alphabetical order 🙄

An odd number is a number that cannot be divisible by 2

Every odd number has an “e” in its spelling. They include:

  • One
  • Three
  • Five
  • Seven
  • Nine

555 in Thailand should sound like “hahaha”. This is because the word 5 means “ha” in Thailand

10! Actually means 10 factorial.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

3628800 seconds is the same as 42 days

42 days is the same as 6 weeks

When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321

With regards to numbers,

Forty is the only number that is spelt with letters arranged in alphabetical order.

One is the only number that is spelt with letters arranged in descending order.


Circumference in mathematics means the distance around the edge of a circle (or a another curverd surface).

Perimeter means the distance around a square or rectangle or polygon.

Circumference is to circle or any other curved surface

Image Credit: Ducksters

Perimeter is to square or rectangle or polygon

Image Credit: Maths is Fun