The sum of three angles of a triangle is 180 degrees. The largest angle of the triangle is 5 times as large as the smallest angle. (continued) The third angle is 18 degrees less than the largest angle. How many degrees are in each of the angles of the triangle? please help me how to solve this problem. i cant understand what it says! please help!

Expert Answers

An illustration of the letter 'A' in a speech bubbles

I'm going to explain this a little more Maganda, because I want you to learn to understand it yourself.

Your math problem talks about all 3 angles of this triangle.  The way they are described they are all related together.  It says the largest angle is 5 times as big as the smallest.  So, you know that if the smallest is X degrees, the largest is 5 times X degrees.  Then they talk about the 3rd angle.  It is 18 degrees less than the largest angle. We already said the largest one is 5X degrees (5 times X).  So, the third one is 5X - 18 degrees.

So, the three angles are:

X, 5X, and (5X-18)

At the beginning of the problem, it says that if you add all 3 angles together the sum is 180 degrees.  So,

X + 5X + (5X - 18) = 180

Since this whole equation is + and -, you can ignore the ( ).

X + 5X + 5X - 18 = 180

put all the Xs together and you get 11X - 18 = 180

You want to get the X all by itself, so you need to do things to BOTH sides of the equation until X is alone. 

First, add 18 to both sides:

11X - 18 + 18 = 180 + 18

- 18 + 18 = 0, so

11X = 198

Now you can divide both sides by 11 to get X alone:

11X divided by 11 = X

198 divided by 11 = 18

so, X = 18

Now you can find out how big each of the 3 angles is, because you know how much X is.

Remember, the 3 angles are X, 5X and (5X-18)

Since X = 18, we know that the angles are 

X = 18

5X = 90

5X-18 = 90 - 18 = 72

We can check the answer to make sure it all adds to 180

18 + 90 + 72 = 180?

YES 

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

Let X = the measure of the smallest angle.  Then the largest angle is 5X, and the remaining angle is 5X-18. So......

X + 5X + (5X-18) = 180

11X-18 = 180

11X=198

X=198/11

Then X=18 degrees.  I'll leave it to you to figure out what that makes the other 2 angles (remember that one is 5X and one is 5X-18)

Approved by eNotes Editorial Team