Mathematics

Angles: What are Angles? Categories of Angles

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

Topics in Mathematics

Angles: Type of angles based on degree measurement Angle Pairs: Types of angle pairs Conversion of Number Bases explained with examples Angles: What are Angles? Categories of Angles Lines and Types in Mathematics Number Base System - Table showing the Number Bases with explanations Mathematics Scheme of Work, SS1, 3rd Term Mathematics Scheme of Work, SS1, 2nd Term Mathematics Scheme of Work, SS1, 1st Term Trigonometry - Sine, Cosine and Tangent explained with worked examples Quadratic Equation - Factorization of Quadratic Equation Algebra - Explanation and Worked Examples on Algebra


Academic Questions in Mathematics

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

Factorize 12a2 - 20a + 3

  • A. (6a - 1)(2a - 3)

  • B. (6a - 1)(2a + 3)

  • C. (6a + 1)(2a - 3)

  • D. (6a + 1)(2a + 3)

  • E. (-6a + 1)(2a - 3)

  • F. (-6a + 1)(2a + 3)

Simplify 10ab + 7ab

  • A. 17ab2

  • B. 17a2b2

  • C. 3ab2

  • D. 3a2b2

  • E. 17ab

  • F 3ab

Which of the following is not a type of angle?

  • A. Right angle

  • B. Left Angle

  • C. Acute Angle

  • D. Complete Angle

  • E. Straight Angle

  • F. Reflex angle

Two lines that can never meet each other are best considered as _____ lines.

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

An angle at exactly 90o is a/an _____ angle.

  • A. acute
  • B. obtuse
  • C. reflex
  • D. right
  • E. complete
  • F. straight

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

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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 is vital in buildings, 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 when taking free throws in basket ball. Similarly, a footballer may utilize 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.

Please read on type of angles here.

As an instance to the above definition, 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 the arms and vertex of an angle:

Arms and Vertex of Angles - Len Academy

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

Angle - Len Academy

Below are some notable points from the above diagram:

  • 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. This implies that angles are measured in degrees and a protractor can be used to achieve this.
  • You can read on Trigonometry (Sine, Cosine and Tangent) here.

 

Representation of Angles

Angles can be represented mainly in two ways. These are:

  1. By using the three letters on the shape of the specific angle. Understand that the angle is formed on the middle letter, (vertex).

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

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

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

Please read on angle pairs here.

 

Categories of Angles

An angle can be categorized as either interior or exterior based on where they are formed with regards to a shape. They are shown in the image below:

Categories of Angles - Len Academy


  • Interior angles are formed inside a shape. In the above diagram, the angle is formed inside a triangle. (A triangle has 3 sides and 3 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.

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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

The opposite sides of a 🎲 dice 🎲 will always give a sum of seven

31,556,926 seconds makes one year

From 0 through 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 in mathematics. Below is its calculation:

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

We can therefore say that 10! equals 6 weeks or 3628800 seconds in mathematics

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


NOTABLE POINTS IN Mathematics

Sides of a right angle triangle - Len Academy

 

The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ

 

Hypotenuse is always the longest side of the triangle.

Opposite is the side opposite the angle (θ)

Adjacent is the shorter side next to the angle (θ)

Each of Sin θ, cos θ and tan θ are the ratio of sides of the right triangle. They are calculated by using the formula (margic word) sohcahtoa:

Sohcahtoa - Len Academy

soh

Sin θ = Opposite/Hypotenuse

cah

Cos θ = Adjacent/Hypotenuse

toa

Tan θ = Opposite/Adjacent

Please read more on sine, cosine and tangent here

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

Circumference of a Circle - Len Academy

Perimeter is to square or rectangle or polygon

Perimeter of a Rectangle - Len Academy