Mathematics

Angles: Type of angles based on degree measurement

len Alfred Ajibola - 02nd March, 2021 @ 11:05 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 click here to see all Questions and Answers

Decagon - Len Academy

What type of polygon is shown in the above image?

  • A. Nonagon

  • B. Decagon

  • C. Octagon

  • D. Hexagon

  • E. Hepagon

  • F. Pentagon

Which of the following is not part of a circle?

  • A. Section

  • B. Sector

  • C. Segment

  • D. Semicircle

  • E. Secant

  • F. Center

Acute Angle - Len Academy

What angle is shown in the above image?

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

An angle greater than 90o but less than 180o is termed _____.

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

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



Classification of Angles:

Angles are generally considered as a part of geometry. It is formed at a place where two line intersects or meet each other; and is measured in degrees.

An angle is defined as a figure formed by two sides of a line (called rays) meeting at a common endpoint (called vertex).

Please the introduction to angles here

Angles are classified into various types based on the following criterias:

  • Based on their degree measurement

  • Based on their pairs (angle pairs)
    Please on angle pairs here.

  • Based on their direction of rotation


Types of angle based on degree measurement

Angles can be determined based on their measurement in degree. To this end, an angle with zero degree (0o) is called a zero angle; and it's formed when the arms of the angle are at the same position.

If we increased the size of the angle to a certain degree, the name of the angle changes automatically. For instance, an angle between 0o through 90o is termed an acute angle but as soon as we increase the size of the angle to 90o, its name changes to a right angle.

You can read on lines and type of lines in mathematics here.

Generally, we are seven types of angles based on their degree measurement. The image below shows six of these:

Types and Names of Angles - Len Academy


Below are explanations on the types of angle based on degree measurement:


  1. Zero Angle: This is an angle that has a measurement of 0o. It is formed when both arms of the angle are at the same position. Below is an image that shows a zero angle.
    Zero Angle - Len Academy

    From the above image, the points P, Q and R are on the same position. As a result, the angle PQR equals zero degree (∠ RPQ = 0o)


  2. Acute Angle: This is an angle whose degree measurement is greater than 0o but less than 90o. Instances of acute angles include 1o, 15o, 30o, 45o, 60o 89o, etc. The image below shows a 60o angle.
    Acute Angle - Len Academy


  3. Right Angle: An angle that is exactly 90o is termed a right angle. For this reason, it's also called a 90o angle (90 degree angle). They are represented by drawing a small box between the vertical and horizontal arms of the angle. See the image below:
    Right Angle - Len Academy


  4. Obtuse Angle: An obtuse angle is always greater than 90o but less than 180o. Examples of obtuse angles are 91o, 110o, 130o, 150o, etc. It is shown in the image below:
    Obtuse Angle - Len Academy

  5. You can read on trigonometry (sine, cosine and tangents) here.


  6. Straight Angle: This is an angle that is exactly 180o. Straight angle may also be termed as an angle on a straight line. See the image below:
    Straight Angle - Len Academy


  7. Reflex Angle: This is an angle whose degree measurement is greater than 180o but less than 360o. Angles that fall within this range includes 181o, 200o, 250o, 359o, etc.
    Reflex Angle - Len Academy

  8. You can attempt various questions and answers for students here.


  9. Complete Angle: This is an angle whose measurement is exactly 360o. Complete angle are also known as full rotation angle:
    Complete Angle - Len Academy

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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 sounds like 'hahaha'. This is because the number '5' means 'ha' in Thailand

In mathematics, 10! means 10 factorial. 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

Interestingly, 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

Let's use algebra to explain the simple statement below:

I am a number. When you subtract 3 from me, the result is 9. what number am I ?

Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.

Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:

  • Let the number be y

  • y - 3 = 9

  • y = 9 + 3

  • y = 12

Please read more on algebra here

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. Below are some points to note:

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 of a Circle - Len Academy

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

Circumference is to circle or any other curved surface

Perimeter of a Rectangle - Len Academy

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

Perimeter is to square or rectangle or polygon