Step by step
The question
Question: In a triangle, the second angle is twice the first.
The third angle is 20° more than the first.
Find the 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.
The right way: x + 2x + (x + 20) = 180.
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.
First we remove the + 20, so 4x is alone.
Then we remove the times 4.
Is x alone now?
Not yet: + 20 is still with x.
How do we remove it?
6 Remove the + 20
To remove + 20, we take away 20.
We do it on both sides, so they stay equal.
+ 20 and − 20 cancel each other.
They make zero.
180 − 20 = 160.
Now we have 4x = 160.
So after step 6: we took away 20, and now we have 4x = 160.
Is x alone now?
Not yet: 4x means 4 times x.
7 Remove the 4
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
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.