Step by step
The question
Question: In a right triangle, one of the two small angles is 30° less than the other.
Find the two small angles.
1 Find what we know
What do we know?
A right triangle has one angle of 90°.
One small angle is 30° less than the other.
What do we want?
The two small angles.
2 Name the unknown
We know the other angles from this one.
So we call one small angle x.
The other small angle is 30° less: x − 30.
Let's draw it.
The angles are x, x − 30 and 90°.
The three angles of a triangle always add up to 180°.
3 Write the equation
In words: the two small angles and the right angle make 180.
So the equation is x + (x − 30) + 90 = 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 = 2x.
−30 + 90 = 60.
Now we have 2x + 60 = 180.
We want x by itself.
Two things are stuck to x: times 2 and + 60.
The + 60 is on the outside, so it comes off first.
Then the times 2.
6 Remove the + 60
To remove + 60, we take away 60.
We do it on both sides, so they stay equal.
+ 60 and − 60 make zero.
Cross them out.
180 − 60 = 120.
Now we have 2x = 120.
7 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
120 divided by 2 is 60.
So x = 60!
8 Answer the question
The other small angle: 60 − 30 = 30.
So the angles are 60° and 30°.
9 Check
Let's check in the story.
All the angles: 60 + 30 + 90 = 180, like a triangle must.
And the other small angle is 30° less, 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.