Step by step
The question
Question: In a triangle, the second angle is 3 times the first.
The third angle is 5 times 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 5 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 3 times the first: 3x.
The third angle is 5 times the first: 5x.
Let's draw it.
The angles are x, 3x and 5x.
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 + 5x = 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 + 3x + 5x = 9x.
Now we have 9x = 180.
5 Remove the 9
9x means 9 times x.
We want just x.
To remove times 9, we divide by 9.
We do it on both sides, so they stay equal.
9 divided by 9 is 1.
So just x is left.
180 divided by 9 is 20.
So x = 20!
6 Answer the question
The second angle: 3 × 20 = 60.
The third angle: 5 × 20 = 100.
So the angles are 20°, 60° and 100°.
7 Check
Let's check in the story.
All the angles: 20 + 60 + 100 = 180, like a triangle must.
And the second angle is 3 times the first, like the story says.
And the third angle is 5 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.