Year 8 Interactive Maths - Second Edition

## Geometry

Geometry is used in astronomy, navigation, surveying and many practical occupations.  Surveyors, architects and engineers often use geometrical drawings.  Navigation by air and sea depends on accurate geometry.

In Year 7, some geometrical facts were considered.  In this section, these basic facts will be revised as they will be used to learn further geometry and develop logical reasoning.

###### Recall that:
• The sum of adjacent angles forming a straight line is 180º.

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

The supplement of a is b because a + b = 180º.
The supplement of b is a because a + b = 180º.

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

The complement of x is y because x + y = 90º.
The complement of y is x because x + y = 90º.

### Method for Finding the Value of a Pronumeral

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

#### Example 1

Use the information given in the diagram to find x.  Give reasons for your answer.

##### Solution:

So, the value of x is 131º.

#### Example 2

Use the information given in the diagram to find x.  Give reasons for your answer.

##### Solution:

So, the value of x is 36º.

#### Example 3

What is the complement of 42º?

##### Solution:

Let xº be the complement of 42º.

So, the complement of 42º is 48º.

#### Example 4

What is the supplement of 48º?

##### Solution:

Let xº be the supplement of 48º.

So, the supplement of 48º is 132º.