CHAPTER EIGHT

Topic 8:

GENERAL AND ANGLE PROPERTIES OF

GEOMETRIC FIGURES

Key words: line segment, transversal, parallel

By the end of this topic, you should be able to:

a. identify different angles.

b. solve problems involving angles on a straight line, angles on transversal and parallel lines.

c. state and use angle properties of polygons in solving problems.

Introduction

In bearings you studied angle turns, and in this topic you will study angles on the straight line, parallel lines and angle properties of polygons. Equipped with the knowledge from this topic, you will be able to solve problems related with angle properties.

You will need to understand clearly what the terms such as turn, halfturn, etc. mean in terms of angles. There are 360° in one complete turn,

so the following are true.

i) Turning from N to S is 180° clockwise or anticlockwise.

ii) Turning from NE to SE is 90° clockwise (or 270° anticlockwise).

iii) Turning clockwise from NE to E is 45°(or 315° anticlockwise).

Example

What angle do you turn through if you turn:

a) from NE to NW anticlockwise?

b) from E to N clockwise?

Solution

c) 90° (or ¼ turn)

d) 270° (¾ turn)

Sub-topic 8.1: Identify Different Angles

Activity 8.1: Identifying objects that form angles

In your groups, work in pairs.

Identify objects in you class, which make 90°, 180°, 360° 

A protractor can be used to measure angles.

Note:

The angle around the circle is 360°.

The angle around a point on a line is 180°.

A right angle is 90° 

Compare your answers with other members of the group and classify them

Exercise

1. For each of the following angles, first estimate the angles and then measure the angle to see how good your estimate was.

2. Draw the following angles

(a) 20° (b) 42°  (c ) 80°  (d) 105°  (e) 170° (f) 200° (g) 275° (h) 305°

3. Immaculate finds out the favourite sports for members of her class.

She works out the angles in the list shown below for a pie chart. Draw the pie chart.

Exercise

1. (a) Draw a triangle with one obtuse angle.

(b) Draw a triangle with no obtuse angles.

2. Draw a four-sided shape with:

a) one reflex angle.

b) two obtuse angles.

Sub- topic 8.2: Angles on a Line and Angles at a Point

Remember that:

a) angles on a line add up to 180° 

And:

b) angles at a point add up to 360° 

These are two important results, which help when finding the size of unknown angles.

Activity 8.2: Identifying angles

Work as individuals

Draw two intersecting lines. Use your mathematical instruments to measure the angles formed at the intersecting point.

i) How many angles have been formed at the point of intersection?

ii) What is the size of each angle formed?

Compare your work with your friends and note your findings.

A polygon is a closed plane figure with straight sides.

Activity 8.3: Identifying the polygons

In pairs:

Find the number of sides of different polygons and their corresponding names. Also determine the number and size of interior and exterior angles of the regular polygons.

Compare your answers with other members’.

Exercise

1. If the vertices of a regular hexagon are joined to the centre of the hexagon, what is the size of each of the six angles at the centre? Use your answer to construct a regular hexagon ABCDEF of side 3cm. Start with a circle of radius 3cm. Measure

the length of the diagonal AC.

2. Find the sum of the interior angles of a polygon with 22 sides.

3. The interior angle of a regular polygon is 1620. How many sides has the polygon?

Activity of Integration

A diagram of a table showing coffee production in Uganda from year

2015 to year 2019