Step by step
The question
Question: In a triangle, the second angle is 25° less than twice the first.
The third angle is twice the first.
Find the three angles.
1 Find what we know
What do we know?
The second angle is 25° less than twice the first.
The third angle is twice 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 25° less than twice the first: 2x − 25.
The third angle is twice the first: 2x.
Let's draw it.
The angles are x, 2x − 25 and 2x.
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 − 25) + 2x = 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 + 2x = 5x.
Now we have 5x − 25 = 180.
We want x by itself.
Two things are stuck to x: times 5 and − 25.
The − 25 is on the outside, so it comes off first.
Then the times 5.
6 Remove the − 25
To remove − 25, we add 25.
We do it on both sides, so they stay equal.
− 25 and + 25 make zero.
Cross them out.
180 + 25 = 205.
Now we have 5x = 205.
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.
205 divided by 5 is 41.
So x = 41!
8 Answer the question
The second angle: 2 × 41 − 25 = 57.
The third angle: 2 × 41 = 82.
So the angles are 41°, 57° and 82°.
9 Check
Let's check in the story.
All the angles: 41 + 57 + 82 = 180, like a triangle must.
And the second angle is 25° less than twice the first, like the story says.
And the third angle is twice 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.