Step by step
The question
Question: In a right triangle, one of the two small angles is 5 times 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 5 times 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 5 times the other: 5x.
Let's draw it.
The angles are x, 5x 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 + 5x + 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 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 + 5x = 6x.
Now we have 6x + 90 = 180.
We want x by itself.
Two things are stuck to x: times 6 and + 90.
The + 90 is on the outside, so it comes off first.
Then the times 6.
5 Remove the + 90
To remove + 90, we take away 90.
We do it on both sides, so they stay equal.
+ 90 and − 90 make zero.
Cross them out.
180 − 90 = 90.
Now we have 6x = 90.
6 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.
90 divided by 6 is 15.
So x = 15!
7 Answer the question
The other small angle: 5 × 15 = 75.
So the angles are 15° and 75°.
8 Check
Let's check in the story.
All the angles: 15 + 75 + 90 = 180, like a triangle must.
And the other small angle is 5 times the other, 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.