Two angles of a triangle are 52° and 71°. Find the third angle. Step by Step

Step by step

The question

Question: find x when the angles in a triangle are 52°, 71° and x.

1 Use the angle fact

The three angles in a triangle always add up to 180°.

So we add them all and make it 180: 52 + 71 + x = 180.

52 + 71 + x = 180

2 Group like terms

The plain numbers go together.

52 + 71 = 123

Now we have 123 + x = 180.

123 + x = 180

Is x alone now?

Not yet: + 123 is still with x.

How do we remove it?

3 Remove the 123

We want x by itself.

The 123 is in the way.

To remove 123, we take away 123.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

~~123~~ + x ~~− 123~~ = 180 − 123

123 and − 123 cancel each other.

They make zero.

180 minus 123 is 57.

So x = 57.

The angle x is 57°.

x = 57

4 Check

Let's check: put x = 57 back and add the angles.

52 + 71 + 57 = 180

They add up to 180°.

So x = 57 is right!

Let's look back.

First: use the angle fact.

Then: group like terms.

Then: remove the 123.

Last: check.

Answer