Angles and Symmetry
Measuring Angles

A protractor can be used to measure or draw angles.

Note

The angle around a complete circle is 360˚.

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

Worked Examples

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˚.

Note

When measuring an angle, start from the 0° which is in line with an arm of the angle.
2

Measure the marked 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°.

Exercises

Estimate the size of each angle, then measure it with a protractor.

(a)

E : °

M = °

(b)

E : °

M = °

(c)

E : °

M = °

(d)

E : °

M = °

(e)

E : °

M = °

(f)

E : °

M = °

Measure these angles.

(a)
°
(b)
°
(c)
°
(d)
°
(e)
°
(f)
°

Measure each named (a, b, c) angle below and add up the angles in each diagram.

(a)
a + b = °
(b)
a + b + c = °
(c)
a + b = °
(d)
a + b + c = °

For each triangle below, measure each interior angle and add up the three angles you obtain.

(a)
A + B + C = °
(b)
A + B + C = °
(c)
A + B + C = °
(d)
A + B + C = °

Measure the interior (inside) angles of these quadrilaterals. In each case find the total sum of the angles.

(a)
a + b + c + d = °
(b)
a + b + c + d = °