Measuring Angles

The objectives of this section are to

Note

The angle around a complete circle is is 360°.

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

A right angle is 90°.

1

Measure the angle CAB in the triangle shown.

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Place a protractor on the triangle as shown.

The angle is measured as 47°.
2

Measure this angle.

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Using a protractor, the smaller angle is measured as 100°.

So

required angle = 360° − 100°
= 260°
3

Draw angles of

(a)

120°

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Draw a horizontal line.

Place a protractor on top of the line and draw a mark at 120°.

Then remove the protractor and draw the angle.
(b)

330°

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To draw the angle of 330°, first subtract 330° from 360°:

360° − 330° = 30°

Draw an angle of 30°.

The larger angle will be 330°.

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

The estimations will not be checked.

(a)
e: ° m: °
(b)
e: ° m: °
(c)
e: ° m: °
(d)
e: ° m: °
(e)
e: ° m: °
(f)
e: ° m: °
(g)
e: ° m: °
(h)
e: ° m: °

Estimate and measure the size of each of these reflex angles.

The estimations will not be checked.

(a)
e: ° m: °
(b)
e: ° m: °
(c)
e: ° m: °
(d)
e: ° m: °
(a)

Measure each of the angles in this pie chart.

Manchester United: °

Arsenal: °

Newcastle: °

Chelsea: °

Other: °

(b)

Which is the most popular of these teams?

(c)

Which is the second most popular team?

In which of these polygons are the angles all the same size?

Find all the angles in each polygon. (You may need to copy the shapes on to paper and extend the lines.)

(a)

Angle at

A: °

B: °

C: °

D: °

E: °

(b)

Angle at

A: °

B: °

C: °

D: °

E: °

F: °

(c)

Angle at

A: °

B: °

C: °

D: °

E: °

F: °

G: °

H: °

(d)

Angle at

A: °

B: °

C: °

D: °

E: °

F: °

G: °

(e)
The polygons angles are all the same size.

Draw the shape below, where O is the centre of the circle. Make the radius of your circle 6 cm.

Measure the distances between AB, BC and AC.

AB: cm

BC: cm

AC: cm