In a triangle, the second angle is 20° more than the first. The… Easy

The question

Question: In a triangle, the second angle is 20° more than the first.

The third angle is twice the first.

Find the three angles.

1 Find what we know

What do we know?

The second angle is 20° more than the first.

The third angle is twice the first.

What do we want?

The three angles.

2 Name the unknown

We know the other angles from the first.

So we call the first angle x.

The second angle is 20° more: x + 20.

The third angle is twice the first: 2x.

Let's draw it.

The angles are x, x + 20 and 2x.

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

3 Write the equation

In words: first plus second plus third makes 180.

So the equation is x + (x + 20) + 2x = 180.

Now we solve it.

Careful!

The angles of a triangle make 180°, not 360°.

360° is all the way round a point.

4 Open the brackets

A bracket with a plus or nothing in front can just be removed.

5 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 = 4x.

Now we have 4x + 20 = 180.

We want x by itself.

Two things are stuck to x: times 4 and + 20.

The + 20 is on the outside, so it comes off first.

Then the times 4.

6 Remove the + 20

To remove + 20, we take away 20.

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

+ 20 and − 20 make zero.

Cross them out.

180 − 20 = 160.

Now we have 4x = 160.

7 Remove the 4

4x means 4 times x.

We want just x.

To remove times 4, we divide by 4.

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

4 divided by 4 is 1.

So just x is left.

160 divided by 4 is 40.

So x = 40!

8 Answer the question

The second angle: 40 + 20 = 60.

The third angle: 2 × 40 = 80.

So the angles are 40°, 60° and 80°.

9 Check

Let's check in the story.

All the angles: 40 + 60 + 80 = 180, like a triangle must.

And the second angle is 20° more, like the story says.

And the third angle is twice the first, like the story says.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved

In a triangle, the second angle is twice the first. The third angle… Medium

The question

Question: In a triangle, the second angle is twice the first.

The third angle is 20° more than the first.

Find the three angles.

1 Find what we know

What do we know?

The second angle is twice the first.

The third angle is 20° more than the first.

What do we want?

The three angles.

2 Name the unknown

We know the other angles from the first.

So we call the first angle x.

The second angle is twice the first: 2x.

The third angle is 20° more: x + 20.

Let's draw it.

The angles are x, 2x and x + 20.

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

3 Write the equation

In words: first plus second plus third makes 180.

So the equation is x + 2x + (x + 20) = 180.

Now we solve it.

Careful!

The angles of a triangle make 180°, not 360°.

360° is all the way round a point.

4 Open the brackets

A bracket with a plus or nothing in front can just be removed.

5 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 + x = 4x.

Now we have 4x + 20 = 180.

We want x by itself.

Two things are stuck to x: times 4 and + 20.

The + 20 is on the outside, so it comes off first.

Then the times 4.

6 Remove the + 20

To remove + 20, we take away 20.

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

+ 20 and − 20 make zero.

Cross them out.

180 − 20 = 160.

Now we have 4x = 160.

7 Remove the 4

4x means 4 times x.

We want just x.

To remove times 4, we divide by 4.

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

4 divided by 4 is 1.

So just x is left.

160 divided by 4 is 40.

So x = 40!

8 Answer the question

The second angle: 2 × 40 = 80.

The third angle: 40 + 20 = 60.

So the angles are 40°, 80° and 60°.

9 Check

Let's check in the story.

All the angles: 40 + 80 + 60 = 180, like a triangle must.

And the second angle is twice the first, like the story says.

And the third angle is 20° more, like the story says.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved

In a right triangle, one of the two small angles is 15° more than… Harder

The question

Question: In a right triangle, one of the two small angles is 15° more than the other.

Find the two small angles.

1 Find what we know

What do we know?

A right triangle has one angle of 90°.

One small angle is 15° more than the other.

What do we want?

The two small angles.

2 Name the unknown

We know the other angles from this one.

So we call one small angle x.

The other small angle is 15° more: x + 15.

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

3 Write the equation

In words: the two small angles and the right angle make 180.

So the equation is x + (x + 15) + 90 = 180.

Now we solve it.

Careful!

The angles of a triangle make 180°, not 360°.

360° is all the way round a point.

4 Open the brackets

A bracket with a plus or nothing in front can just be removed.

5 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.

Plain numbers go together.

x + x = 2x.

15 + 90 = 105.

Now we have 2x + 105 = 180.

We want x by itself.

Two things are stuck to x: times 2 and + 105.

The + 105 is on the outside, so it comes off first.

Then the times 2.

6 Remove the + 105

To remove + 105, we take away 105.

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

+ 105 and − 105 make zero.

Cross them out.

180 − 105 = 75.

Now we have 2x = 75.

7 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.

So x = 75/2!

8 Answer the question

The other small angle: 37.5 + 15 = 52.5.

So the angles are 37.5° and 52.5°.

9 Check

Let's check in the story.

All the angles: 37.5 + 52.5 + 90 = 180, like a triangle must.

And the other small angle is 15° more, like the story says.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved