Step by step
The question
Question: In a triangle, the second angle is 30° more than twice the first.
The third angle is 3 times the first.
Find the three angles.
1 Find what we know
What do we know?
The second angle is 30° more than twice the first.
The third angle is 3 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 30° more than twice the first: 2x + 30.
The third angle is 3 times the first: 3x.
Let's draw it.
The angles are x, 2x + 30 and 3x.
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 + (2x + 30) + 3x = 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 + 2x + 3x = 6x.
Now we have 6x + 30 = 180.
We want x by itself.
Two things are stuck to x: times 6 and + 30.
The + 30 is on the outside, so it comes off first.
Then the times 6.
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 6x = 150.
7 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
So just x is left.
150 divided by 6 is 25.
So x = 25!
8 Answer the question
The second angle: 2 × 25 + 30 = 80.
The third angle: 3 × 25 = 75.
So the angles are 25°, 80° and 75°.
9 Check
Let's check in the story.
All the angles: 25 + 80 + 75 = 180, like a triangle must.
And the second angle is 30° more than twice the first, like the story says.
And the third angle is 3 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.