Isosceles triangle top angle 40 Easy

The question

Question: find the base angles x of an isosceles triangle with top angle 40°.

1 Use the isosceles fact

Isosceles means two sides are equal.

The small marks show which two.

Fold it on the dashed line, from the top to the middle of the base.

The two halves fit exactly.

So the two angles at the base fit on each other.

The base angles are equal.

So the other base angle is x too.

2 Use the angle fact

The three angles in a triangle add up to 180°: x + x + 40 = 180.

Careful!

There are two base angles.

Both go in the sum.

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

x + x = 2x.

Now we have 2x + 40 = 180.

We want x by itself.

Two things are stuck to x: times 2 and + 40.

The + 40 is on the outside, so it comes off first.

Then the times 2.

4 Remove the + 40

To remove + 40, we take away 40.

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.

+ 40 and − 40 make zero.

Cross them out.

180 − 40 = 140.

Now we have 2x = 140.

5 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just x is left.

140 divided by 2 is 70.

So x = 70!

6 Check

Let's check: put x = 70 back and add the three angles.

They add up to 180°.

So x = 70 is right!

Let's look back.

First: use the isosceles fact.

Then: use the angle fact.

Then: group like terms.

Then: remove the + 40.

Then: remove the 2.

Last: check.

▶ Watch it solved

Isosceles triangle top angle 36 Medium

The question

Question: find the base angles x of an isosceles triangle with top angle 36°.

1 Use the isosceles fact

Isosceles means two sides are equal.

The small marks show which two.

Fold it on the dashed line, from the top to the middle of the base.

The two halves fit exactly.

So the two angles at the base fit on each other.

The base angles are equal.

So the other base angle is x too.

2 Use the angle fact

The three angles in a triangle add up to 180°: x + x + 36 = 180.

Careful!

There are two base angles.

Both go in the sum.

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

x + x = 2x.

Now we have 2x + 36 = 180.

We want x by itself.

Two things are stuck to x: times 2 and + 36.

The + 36 is on the outside, so it comes off first.

Then the times 2.

4 Remove the + 36

To remove + 36, we take away 36.

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.

+ 36 and − 36 make zero.

Cross them out.

180 − 36 = 144.

Now we have 2x = 144.

5 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just x is left.

144 divided by 2 is 72.

So x = 72!

6 Check

Let's check: put x = 72 back and add the three angles.

They add up to 180°.

So x = 72 is right!

Let's look back.

First: use the isosceles fact.

Then: use the angle fact.

Then: group like terms.

Then: remove the + 36.

Then: remove the 2.

Last: check.

▶ Watch it solved

Isosceles triangle top angle x, base angle 2x Harder

The question

Question: find x.

An isosceles triangle has top angle x and base angle 2x.

1 Use the isosceles fact

Isosceles means two sides are equal.

The small marks show which two.

Fold it on the dashed line, from the top to the middle of the base.

The two halves fit exactly.

So the two angles at the base fit on each other.

The base angles are equal.

So the other base angle is 2x too.

2 Use the angle fact

The three angles in a triangle add up to 180°: x + 2x + 2x = 180.

Careful!

There are two base angles.

Both go in the sum.

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

x + 2x + 2x = 5x.

Now we have 5x = 180.

4 Remove the 5

5x means 5 times x.

We want just x.

To remove times 5, we divide by 5.

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.

5 divided by 5 is 1.

So just x is left.

180 divided by 5 is 36.

So x = 36!

5 Check

Let's check: put x = 36 back and add the three angles.

They add up to 180°.

So x = 36 is right!

Let's look back.

First: use the isosceles fact.

Then: use the angle fact.

Then: group like terms.

Then: remove the 5.

Last: check.

▶ Watch it solved