The data set in Table 7 (section 1.8) comprised non-numerical or categorical data. Such data often appear in newspaper reports and are usually represented as one or other of two types of graphical display, one type is called a pie chart and the other a bar chart; these are arguably the graphical displays most familiar to the general public, and are certainly ones that you will have seen before. Pie charts are discussed in section 2.2 and bar charts in section 2.4. Some problems
Author(s): The Open University

A quadrilateral is a shape with four straight sides.
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If several angles make up a half turn, then the sum of those angles must be Ã—Â 360Â°Â =Â 180Â°. Therefore, in the following diagram, Î± + Î² + Î³ + Î´Â =Â 180Â°.

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Another useful property to remember is that one complete turn is 360Â°. This means that when there are several angles making up a complete turn, the sum of those angles must be 360Â°.

For instance, if the angles turned by a Big Wheel at a fairground as it picks up passengers were Î±, Î², Î³ and Î´ as shown in the diagram below, then Î± + Î² + Î³ + Î´Â =Â 360Â°.

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Very often, angles in a shape are determined by the geometric properties of that shape. For example, a square has four right angles. So, when you know a shape is a square, you do not need to measure its angles to know that they are 90Â°. The rest of this section will look at the properties of shapes that enable you to deduce and calculate angles rather than measure them. You may like to add these properties to your notes.

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## Question 1

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To measure an angle you need a protractor. The protractor shown here is a semicircle that is graduated to measure angles from 0Â° to 180Â°. It is also possible to buy circular protractors that measure angles from 0Â° to 360Â°.

Author(s): The Open University

## Question 1

What angles do the hour hand and the minute hand of a clock turn through in five hours?

Every hour the minute hand turns th
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In everyday language, the word â€˜angleâ€™ is often used to mean the space between two lines (â€˜The two roads met at a sharp angleâ€™) or a rotation (â€˜Turn the wheel through a large angleâ€™). Both of these senses are used in mathematics, but it is probably easier to start by thinking of an angle in terms of the second of these â€“ as a rotation.

The diagram below shows a fixed arm and a rotating arm (with the arrow), which are joined together at O, forming an angle between th
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After studying this course, you should be able to:

• understand geometrical terminology for angles, triangles, quadrilaterals and circles

• measure angles using a protractor

• use geometrical results to determine unknown angles

• recognise line and rotational symmetries

• find the areas of triangles, quadrilaterals and circles and shapes based on these.

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All written material contained within this course originated at the Open University

Course image: HÃ¥kan DahlstrÃ¶m in Flickr made available under Creative Commons Attribution 2.0 Licence.

Don't miss out:

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## Study another free course

There are more thanÂ 800 coursesÂ on OpenLearnÂ for you to
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This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.Â

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## SAQ 26

Find the distance between the numbers 2 âˆ’ i and 1Â +Â 3i.

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In this section we shall define the complex number system as the set RÂ Ã—Â R (the Cartesian product of the set of reals, R, with itself) with suitable addition and multiplication operations. We shall define the real and imaginary parts of a complex number and compare the properties of the complex number system with those of the real number system, particularly from the point of view of analysis.

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## Activity 26

• (a) What is 40% as a fraction?

• (b) What isÂ Â
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## Activity 12

A recipe for four people calls for Author(s): The Open University

Proportion is another way of expressing notions of part and whole. You might say that the proportion of village inhabitants who are children is a quarter, or that the proportion of fruit juice in the punch is two thirds, or that the proportion of sand in the concrete is three quarters.

All these examples involve the fractions Author(s): The Open University

## Activity 8

Which is greater, 1.2 minutes or 70 seconds?