Operations with Angles

While discussing addition metaphors, we discussed about various entities which could be added. Angles is one of them.

Addition of Angles

How do you add two angles?

It can be intuitively realized that angles can be added only if they are “adjacent”. The angle formed by these non-common arms is the sum of the individual angles.

When the sum of 2 adjacent angles is one right angle, the angles are called Complementary angles.

When the sum of 2 adjacent angles is two right angles (or a Straight angle) the angles are called Supplementary angles.

When 2 adjacent angles are supplementary, we can say that both the non-common arms are collinear.

Subtraction of Angles

We can see that to find the difference between 2 angles, we have to do it in a slightly different manner from the case of adding them.

Here also both vertices should coincide and one of the arms must coincide. But the non-common arms must be on the same side of the common arm. Here again the angle formed by the non-common arms is the difference between the individual angles.

Comparison of Angles

Two angles can be compared by the same procedure used for finding the difference between them.

Activities Using Set Squares

Students can get a lot of practice in adding and subtracting angles with the pair of Set Squares in the geometry box. Between them, the set squares have the following angles; 30, 45, 60 & 90.

Using the idea of sum/difference of these angles, students can form all angles from 15 to 165 (in steps of 15) using both the set squares.