How_To_Be_Good_At_Math

GEOMETRY • OPPOSITE ANGLES 237

d

e

a

c

b

Finding missing angles

When two lines intersect, if we know the size of one

angle, we can work out the sizes of all the others.

d db

a a

c

c c

b

b

140°

150°

Add a and b

to make d's

opposite angle

Angles b and d

are opposite

and equal

30°

30° 30°

30°

30° 30°

30°

Angles a and b are on

a straight line

Remember,

d + e = 180°

a

We can use what we know about

angles on a straight line to work out

angle a. We know that a + b = 180°, so

a must be 180° − 30°. So a = 150°.

Angles a and c are opposite,

so we know that means they

are equal. So c is 150°.

These two lines intersect, creating

two pairs of opposite angles. We

know that angle d is 30°.

Angles b and d are opposite

each other, so we know that

angle b must be 30°, too.

TRY IT OUT

Angles brainteaser

Can you work out these missing

angles? Use what you know about

the size of a right angle, the angles

on a straight line, and that

opposite angles are equal.

b d d

Answers on page 320

236_237_Opposite_angles.indd 237 29/02/2016 18:05