Step by step
The question
Question: In a triangle, the second angle is 30° less than the first.
The third angle is 30° more than the first.
Find the three angles.
1 Find what we know
What do we know?
The second angle is 30° less than the first.
The third angle is 30° 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 30° less: x − 30.
The third angle is 30° more: x + 30.
Let's draw it.
The angles are x, x − 30 and x + 30.
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 − 30) + (x + 30) = 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.
−30 + 30 = 0.
Now we have 3x = 180.
6 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.
180 divided by 3 is 60.
So x = 60!
7 Answer the question
The second angle: 60 − 30 = 30.
The third angle: 60 + 30 = 90.
So the angles are 60°, 30° and 90°.
8 Check
Let's check in the story.
All the angles: 60 + 30 + 90 = 180, like a triangle must.
And the second angle is 30° less, like the story says.
And the third angle is 30° 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.