Step by step
The question
Question: In a triangle, the second angle is 5 times the first.
The third angle is 4 times the first.
Find the three angles.
1 Find what we know
What do we know?
The second angle is 5 times the first.
The third angle is 4 times 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 5 times the first: 5x.
The third angle is 4 times the first: 4x.
Let's draw it.
The angles are x, 5x and 4x.
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 + 5x + 4x = 180.
Now we solve it.
Careful!
The angles of a triangle make 180°, not 360°.
360° is all the way round a point.
4 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 + 5x + 4x = 10x.
Now we have 10x = 180.
5 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so they stay equal.
10 divided by 10 is 1.
So just x is left.
180 divided by 10 is 18.
So x = 18!
6 Answer the question
The second angle: 5 × 18 = 90.
The third angle: 4 × 18 = 72.
So the angles are 18°, 90° and 72°.
7 Check
Let's check in the story.
All the angles: 18 + 90 + 72 = 180, like a triangle must.
And the second angle is 5 times the first, like the story says.
And the third angle is 4 times 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.