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Year 7 Interactive Maths - Second Edition


Calculating the Size of Angles

We will next consider adjacent angles, supplementary angles, complementary angles, vertically opposite angles and angles forming a circle.


Adjacent Angles

Angles that lie on either side of a common arm are said to be adjacent.

Adjacent angles

E.g.  Angle AOB and angle BOC have the arm BO in common.
So, angle AOB and angle BOC are adjacent angles.


Remember:

The sum of adjacent angles forming a straight line is 180.  Two such angles are also known as supplementary adjacent angles.

Supplementary angles are introduced below.


Example 3

Use the information given in the diagram to find x.

Make use of the sum of adjacent angles

Solution:

By applying the sum of supplementary adjacent angles, we find that x equals 136

So, the value of x is 136.


Example 4

Use the information given in the diagram to find x.

Make use of the sum of adjacent angles

Solution:

By applying the sum of supplementary adjacent angles, we find that x equals 18

So, the value of x is 18.


Supplementary Angles

If the sum of two angles adds up to 180, then the angles are said to be supplementary.

Supplementary angles

The supplement of 40 is 140.
The supplement of 140 is 40.


Complementary Angles

If the sum of two angles adds up to 90, then the angles are said to be complementary.

Complementary angles

The complement of 55 is 35.
The complement of 35 is 55.


Example 5

What is the complement of 38?

Solution:

Complementary angles add up to 90 degrees

The complement of 38 is 52.


Method for Finding the Value of a Pronumeral

To find the value of the pronumeral from the given information, write an equation.  Then solve the equation and write the answer in words.

Example 6

What is the supplement of 38?

Solution:

Supplementary angles add up to 180 degrees

The supplement of 38 is 142


Key Terms

adjacent angles, supplementary adjacent angles, supplementary angles, complementary angles


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