Step by step
The question
Question: In a triangle, the second angle is 10° more than 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 10° more than 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 10° more: x + 10.
The third angle is 20° more: x + 20.
Let's draw it.
The angles are x, x + 10 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 + (x + 10) + (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.
Plain numbers go together.
x + x + x = 3x.
10 + 20 = 30.
Now we have 3x + 30 = 180.
We want x by itself.
Two things are stuck to x: times 3 and + 30.
The + 30 is on the outside, so it comes off first.
Then the times 3.
6 Remove the + 30
To remove + 30, we take away 30.
We do it on both sides, so they stay equal.
+ 30 and − 30 make zero.
Cross them out.
180 − 30 = 150.
Now we have 3x = 150.
7 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
150 divided by 3 is 50.
So x = 50!
8 Answer the question
The second angle: 50 + 10 = 60.
The third angle: 50 + 20 = 70.
So the angles are 50°, 60° and 70°.
9 Check
Let's check in the story.
All the angles: 50 + 60 + 70 = 180, like a triangle must.
And the second angle is 10° more, 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.