Angles are the space between two lines which connect at a point, measured in degrees ($\degree$). They are grouped as acute, obtuse, reflex or right-angles. Angles are measured with a protractor and are always between $0\degree$and $360\degree$.

Types of angles

Acute angles are angles less than $90\degree$.

Right-angles are angles which are exactly $90\degree$. You can see right-angles in many places, such as the corner of a table or a square.

Obtuse angles are angles which are greater than $90\degree$ but less than $180\degree$.

Reflex angles are angles which are greater than $180\degree$.

Measuring angles

To measure angles, you can use a tool called a protractor.

Procedure

1.

When two lines meet at a point they form an angle. To measure this angle, line up the point the lines meet to the centre cross of the protractor. Make sure that one of the lines on the angle is lined up with the zero line on the protractor.

2.

See which number the other line runs through. This will be your measurement.

3.

You will see the line running through two different numbers. This is because a protractor has two sets of numbers, the inside starting from the right and the outside starting from the left. Make sure to only take the reading from the number which is on the same set as the zero you started from. If your zero is on the right, use the inside numbers. If the zero is on the left, use the outside numbers.

Note: If one of the lines is not running along the zero line you won't get an accurate measurement.

Example 1

Measure the angle shown below

Line up the cross-section of the protractor to the corner of the angle. Align the bottom line with the zero line.

As the zero is on the inside, go along the protractor from the inside and stop when you have reached the other line.

Therefore the angle is $\underline{45\degree}$.

Drawing angles

Once you have learned how to measure an angle, drawing them becomes very simple.

Procedure

1.

Draw a straight base line where your angle will start from (in some exercises this will already be drawn for you).

2.

Line up the cross-section of the protractor to the point you want your angle to begin, and make a mark on the paper.

3.

Starting from the zero point, work your way around the protractor to the angle you would like to draw and make another mark on the paper.

4.

Remove the protractor and use a ruler to connect the two marks you made.

Note: Always measure the angle you draw afterwards to make sure you did not make any mistakes.

Example 2

Draw a $40\degree$angle

Draw a straight base line, and line up the protractor to the point you would like the angle to begin and make a mark on the paper. Go along the zero line to $40\degree$ and make a mark on the paper. Remove the protractor, then use a ruler to connect your angle mark to your starting point mark. Check your drawing with a protractor to make sure you've drawn the angle correctly.

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Unit 1

Right angles, acute and obtuse angles

Unit 2

Measuring angles in degrees

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Unit 3

Drawing and measuring angles with a protractor

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FAQs - Frequently Asked Questions

What is a reflex angle?

Reflex angles are angles which are greater than 180°.

What is a right-angle?

Right-angles are angles which are exactly 90°.

What instrument is used to measure angles?

To measure angles, you can use a tool called a protractor.