Chapter 20

Angles

Objectives

Names of Angles Measuring Angles Drawing Angles Angles at a Point Complimentary Angles Supplementary Angles Parallel Lines & Angles Compass Points Bearings – Reading & Drawing Scale Diagrams

Types & Names

• Acute – less than 90o

• Right angle – 90o

• Obtuse – between 90o and 180o

• Straight line – 180o

• Reflex – between 180o and 360o

• Complete turn - 360o

Angle Rules

• Angles at a point add to 360o

• Complementary angles add to 90o

• Supplementary angles add to 180o

• Vertically opposite angles are equal

Examples

1.

3.

5.

2.

4.

6.

Parallel Lines

• Parallel lines never meet

• Corresponding angles are equal

• Alternate angles are equal

• Interior angles add to 180o

Examples

1.

3.

2.

4.

Naming Angles

• Use 3 letters with the middle letter at the angle point

Examples

1. 2.

3. 4.

Direction & Compass Points

Bearings

• All bearings must have 3 figures

• All bearings are measured clockwise from North

Back Bearings

Examples

1. 2.

Scale Drawings

• If units are not denoted they are assumed to be the same

• Eg 1:10 000• Eg 1cm to 10 km

Examples

1. A plan of a boat is 1:65. If the width on the plan is 20 cm, what is the actual length?

2. The scale on a map is 1:200. A field is 60m long. What is it’s width on the map?

Drawing Scale Drawings

Example

1. A boat sails on a course of 040o for 5km and then a further 3km on a bearing of 120o. Find by scale drawing

(a) The distance the boat is from the starting point.

(b) The bearing on which it must return to sail directly back to the start