How_To_Be_Good_At_Math

242 GEOMETRY • CALCULATING ANGLES INSIDE TRIANGLES

Calculating angles

inside triangles

The third triangle is

different again but we

still get the same answer:

40° + 50° + 90° = 180°

In this triangle, two

of the angles are the

same. When we add all

three angles we get:

70° + 70° + 40° = 180°

Prove it!

One way to test that the angles inside a triangle add up to 180° is

to take the three corners from a triangle and see how perfectly they

fit along a straight line. We already know a straight line is 180°.

Tear each

corner off

Cut a triangle out of paper. The

sides and angles can be any size.

Now tear off the three corners.

Make all three corners touch.

Look how they form a straight

line, which we know is 180°.

Rotate the three corners so that

you can bring them together.

Look at the

straight line

This triangle has

angles of 60°,

30°, and 90°. Let’s

add them up:

60° + 30° + 90° = 180°

Look at the three sails

on this boat. Each one

is a triangle, but all three

triangles are different.

The special thing about the angles

inside a triangle is that they always add

up to 180°. It doesn’t matter whether

the lengths of the sides and angles

are the same or different – when

we add the angles up, we always

get the same answer.

60º 90º 90º 50º

30º

40º

40º

70º

70º

242_243_Calculating_with_Angles_inside_triangles.indd 242 29/02/2016 18:05