Step by step
The question
Question: In a triangle, the second angle is 3 times the first.
The third angle is 40° more than the first.
Find the three angles.
1 Find what we know
What do we know?
The second angle is 3 times the first.
The third angle is 40° 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 3 times the first: 3x.
The third angle is 40° more: x + 40.
Let's draw it.
The angles are x, 3x and x + 40.
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 + 3x + (x + 40) = 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 + 3x + x = 5x.
Now we have 5x + 40 = 180.
We want x by itself.
Two things are stuck to x: times 5 and + 40.
The + 40 is on the outside, so it comes off first.
Then the times 5.
6 Remove the + 40
To remove + 40, we take away 40.
We do it on both sides, so they stay equal.
+ 40 and − 40 make zero.
Cross them out.
180 − 40 = 140.
Now we have 5x = 140.
7 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, so they stay equal.
5 divided by 5 is 1.
So just x is left.
140 divided by 5 is 28.
So x = 28!
8 Answer the question
The second angle: 3 × 28 = 84.
The third angle: 28 + 40 = 68.
So the angles are 28°, 84° and 68°.
9 Check
Let's check in the story.
All the angles: 28 + 84 + 68 = 180, like a triangle must.
And the second angle is 3 times the first, like the story says.
And the third angle is 40° 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.