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Introduction to Angles

Angles are formed when two rays have the same end point. This common end point is called the vertex.

Angle ABCAngle ABC

The angle ABC is written as  LABC. Other ways of representing the LABC  is LB, hat{B}, or LCBA.

B is the vertex and must be in the middle. AB and BC are called arms of the angle.

Here are some other types of angles.

Note:

  • LB or hat{B} is used only if the angle has 2 arms.
  • Also, we need to be careful to represent the angle as LB or hat{B} when the point B is the vertex for more than one angle. Since there are two angles LABC and LCBD sharing the same vertex B, we cannot represent the angle as LB or hat{B}

Common vertex angleAdjacent angles

Adjacent angles:

When we have a common arm, say BC (in the above diagram) at vertex B, LABC (or LCBA) and LCBD (or LDBC) are called adjacent angles.

 

Complementary angles:

When adjacent angles add up to 90°, the two angles are then said to be complementary angles; they will then make a right angled triangle (= 90º).

Here LABC and LCBD, (50º and 40° respectively) are complementary angles. We say 50º is a complement of 40º and vice versa.

introduction to angles-complementary angles

Straight line (or supplementary angles):

This is a straight line, and it measures 180°.

introduction to angles-straight line

When a pair of angles that have a sum of 180°, then they are called supplementary angles. Here LABC (= 130°) and LABD (=50°) add up to 180°(straight angle), and hence are supplementary angles. 50º is supplement of 130º.

introduction to angles-supplementary angles

 

Vertically opposite angles:

When two straight lines intersect, four angles are formed, viz. LABE, LEBC, LCBD and LDBA. Of these four angles, LEBC and LDBA are equal and vertically opposite each other. Similarly, LABE and LCBD are equal and vertically opposite each other.

introduction to angles-vertically opposite angles

 

Angle at a point:

Finally, when two or more angles with a common vertex move around in a circle (or form a revolution), they will add up to 360°.

introduction to angles-revolution

Here’s some other types of angles