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5.3 Solving angle problems

5.3 Solving angle problems

What do you remember about angles?

t !e sum of the angles at a point or on a straight line.
t Angle properties of triangles and special quadrilaterals, such as a
parallelogram.

t !e sum of the angles of a quadrilateral and other polygons.
t Properties of parallel lines, including corresponding angles and
alternate angles.

!ere is a summary of all these topics on the "rst page of this unit.

In this section you will practise using the facts you know to solve problems.

As well as "nding the answer, you also need to explain your reasoning to show why the answer is
correct. You can use words or diagrams to do this.
Diagrams in this exercise are not drawn accurately.

Worked example 5.3
C B A
In the diagram, CA is parallel to EF. 120° 100°
a Work out the size of the angle labelled f °.
b Work out the value of d. D d°

130° f °
E F

a The angle marked f ° is 100°. CA and EF are parallel so angles ABF (100°) and BFE
(f °) are alternate angles. They are equal.
b Angle CBF = 80° Angles on a straight line add up to 180°. Now we know
four of the angles of the pentagon.
The angles of a pentagon add up to 540°. The sum of the angles of a pentagon is 3 × 180°.
So d = 540 − (120 + 80 + 100 + 130) Subtract the other four angles of the pentagon from 540.
= 110

) Exercise 5.3 Give reasons for your answers in all the questions in this exercise.

1 ABC is a triangle and DE is parallel to BC. A
a Work out the value of a.
b Work out the value of b. 35°

a° 40°
D E

b°
B C
5 Shapes 45