Mathematics

Angle Pairs: Types of angle pairs

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 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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Types of angle pairs:

An angle is a figure formed when the two sides of a line (termed rays) meet at the vertex. Recall that the vertex is a common endpoint where the two sides of a line (rays or arms) meet.

Please read more on the introduction to angles here.

In geometry, we have a category of angles known as angle pairs (or pairs of angles). Such angles are described as angle pairs because they always occur in twos. Their occurrence in pair will also show a specific property in the respective angles.

Note: Recall that angles can also be classified based on their degree measurement.

Please read on classification of angles based on degree measurement here.


Below are types or classifications of angles based on their occurrence in pairs:


  1. Complementary Angles: These are two angles (or pair angles) that sum exactly to 90o. Understand that a 90o angle is also termed a right angle. For this reason, the 30o and 60o angles (sharing a common endpoint) will be considered as complementary angles because they sum up to a right angle (90o). They are shown in the image below:
    Complementary Angles - Len Academy


  2. Supplementary Angles: These are pair angles whose sum equals 180o. In the image below, notice that the angles (120o and 60o) are supplementary because they sum up to 180o.
    Supplementary Angles - Len Academy

    Recall that the 180o angle is also termed a straight angle or angle on a straight line.


  3. Adjacent Angles: Two angles are said to be adjacent when they share the same arm and vertex which does not overlap. In the image below, notice that the three arms (or rays) of the angle do not overlap and they also meet at a common endpoint called the vertex.
    Adjacent Angles - Len Academy

  4. You can read on factorization of quadratic equation here.


  5. Corresponding Angles: These are pair angles present on the same side of the vertex when a line intersects a pair of parallel lines. It is noteworthy to state that corresponding angles are always on the same side. See the image below:
    Corresponding Angles - Len Academy

    Corresponding angles are always equal to each other when the lines are parallel. However, the line that intersects both parallel lines is called the transversal.


  6. Alternate Interior Angles: They are pair angles formed when a line intersects or cuts two parallel lines. The intersecting line is called the transversal. Alternate interior angles are in opposition to each other. Also, both alternating angles are always equal when the lines are parallel.
    Alternate Interior Angles - Len Academy

    The Alternate Interior Angles Theorem states that if two lines are parallel, then the pairs of alternate interior angles are congruent.

    Note: The term congruent in the above theorem implies that both angles are equal, identical in form and coincides exactly when superimposed.

    You can read on number base system here.


  7. Alternate Exterior Angles: In simple terms, the alternate exterior angles are the vertical angles of the alternate interior angles. They are always equivalent or the same when the transversal intersects two parallel lines. They are shown in the image below:
    Alternate Exterior Angles - Len Academy

    You can read motivational quotes for students here.


  8. Vertically Opposite Angle: These are angles formed at a point where two opposite lines cross or intersects each other centrally. The term vertical (in vertically opposite angles) implies that both angles share the same vertex; and not necessarily the common up-down meaning often ascribed to vertical.

    The image below shows two pairs of vertically opposite angles. Notice that the sum of degree measurement in vertically opposite angles is always lesser than 360o with both angles having equal degree measurements.
    Vertically Opposite Angles - Len Academy

    Vertically opposite angles may simple be referred to as vertical angles.

    Instances where vertically opposite angles are present in real-life include a pair of open scissors, railroad crossing signs, open pliers, etc.

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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 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

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