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