Drawing and measuring angles - KS3 Maths

Key points

An angle is the amount of turn between two lines. Angles are measured in degrees with the symbol °.
Angles can be sorted into types depending on how big they are: , , , and .
Angles can be labelled with 3 letters (eg DEF) to show which angle is being referred to. The middle letter is where the angle is, while the other two letters show which lines enclose the angle.
When measuring or drawing angles, count from zero on the . This could mean following the inside row or the outside row of numbers, depending on the position of the angle.

Angles are based on parts of a full turn, which is 360°.

A quarter turn is 90° and is called a right angle.

A half turn is 180° and is known as a straight angle (or angle on a straight line).

A three-quarter turn is 270°.

The size of an angle can be without using a protractor. To do this, the type of angle should be considered.

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The four angles that are used most often are those based on quarter turns.
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These are all right angles as they are all a quarter turn (90°). To show an angle is a right angle, a square box is used instead of a curved line.
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Acute angles are less than 90°. Both these angles are acute because the line has turned less than 90°.
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These acute angles are the same. It does not matter how long the lines are because it is the amount of turn that is being measured.
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An obtuse angle is between 90° and 180°. Both of these angles are obtuse. Without using a protractor, a good estimate for the first angle is 135° because it is midway between 90° and 180°. A good estimate for the second angle would be 170° because it is almost a half turn (180°).
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Reflex angles are greater than 180° as they go further than a half turn. This angle has gone past 270° (three quarter turns) but is closer to 270° than 360°. A good estimate for this angle would be 300°.

For each example, name the type of angle and estimate its size (to the nearest 10°).

When there are lots of lines on a diagram, it is handy to use letters to make it clear which angle is being talked about.

Angle CAB would be the angle made when travelling from point C to point A to point B.

A protractor is used to measure angles.

To measure an acute or obtuse angle, follow these steps:

Place the cross on the protractor over the vertex (corner) of the angle.
Place the bottom line on the protractor along one of the lines of the angle. There will be a zero on the line.
Check whether the zero is on the inside row (closer to the centre of the protractor) or the outside row (closer to the edge of the protractor).
Follow the numbers from zero around the protractor to read off the angle measurement. The angle could be measured in a or direction depending on which row is being followed.

To measure a reflex angle, measure the acute or obtuse angle instead and subtract this from 360°.

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Angle LMN is shown on the left. If the reflex angle LMN is needed instead, it will be labelled specifically as ‘reflex angle LMN’, like the picture on the right-hand side.
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To measure the angle LMN, the cross of the protractor should be placed at the point where the two lines meet, and the bottom line of the protractor should cover one of the lines.
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Looking at the bottom line (NM), the zero that touches the line is on the outside row. Follow the outside numbers in a clockwise direction to the other line (LM). This angle is 60°.
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To measure the angle PQR, the zero that touches the line PQ is on the inside row. Follow the inside numbers in an anti-clockwise direction to the other line (QR). Read the scale carefully, especially when travelling anti-clockwise. This angle goes past 130°. The angle is 132°.
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To measure the reflex angle SUV, it is easier to measure the obtuse angle SUV and subtract this from 360°. The obtuse angle SUV can be measured anti-clockwise from the line SU to get 120°. Then, subtract this angle from 360° to find the reflex angle. The reflex angle SUV = 360° − 120° = 240°.

Question 1:

Measure the angle ABC.

Question 2:

Measure the reflex angle DEF.

To draw an acute or obtuse angle, for example PQR = 60°, follow these steps:

Draw the line QR.
Place the cross on the protractor on the point Q, and the bottom line over the line QR.
Use the protractor to measure 60° from the zero line, and make a mark at 60°. This is point P.
Draw a line from the mark to point Q.

Protractors usually stop at 180°, which means reflex angles cannot be drawn by just following this method.

To draw a reflex angle, for example PQR = 300°, calculate what the acute angle PQR would be instead.

The acute angle is 360° \(-\) 300° = 60°.

Then, follow the same steps as above to draw an angle of PQR = 60°, then label the reflex angle as 300°.

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To draw a reflex angle such as PQR = 300°, it is easier to draw the ‘other’ angle, then show the reflex angle as the angle required. The ‘other’ angle is found by subtracting 300° from 360°. 360° – 300° = 60°.
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Draw the line QR with a ruler.
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Place the protractor on the line QR. Make sure that the cross of the protractor is on the point Q. Measure an angle of 60° by following the numbers anti-clockwise from the zero on the line QR. Make a mark at 60° and label this point P.
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Remove the protractor and join point Q to point P with a line using a ruler.
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To show the angle of 300°, mark the reflex angle.