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5.3 Solving angle problems

5.3 Solving angle problems

You already know how to calculate angles, but in solving problems you need to give reasons for
your answers.
Here are some of the facts you could use.
r The sum of the angles on a straight line is 180 °.
r The sum of the angles round a point is 360 °.
r Vertically opposite angles are equal.
r Corresponding angles are equal.
r Alternate angles are equal.
r The angle sum of a triangle is 180 °.
r The exterior angle of a triangle is the sum of the two opposite interior angles.
r The angle sum of a quadrilateral is 360 °.

Worked example 5

Show that the opposite angles of a parallelogram are equal. Give a reason for any statement you make.

Draw a parallelogram with one side extended. Opposite sides are parallel. d° c°
a and x are equal because they Using the sides with
are corresponding angles. two arrows.
c and x are equal because they are Using the sides with y° a° b° x°
alternate angles. one arrow.
This means a and c must be equal. This is the first pair.
In the same way, b and d are equal. This is the second pair.

The first step in the worked example was to draw a diagram and label the angles. You often need to do
this when you are explaining a geometrical result.
Always give a reason for any statement you make.

✦ Exercise 5.3

1 Maha has made some mistakes in her homework.
Explain why her angles cannot all be correct.

In the diagram, KL and MN
are straight line segments.

N L
150°
30° 20°
K 160°
M

5 Angles 57