# 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...

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?

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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

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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)

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First let " x " be the measure of the smallest angle, then let " 5x " represent the largest angle of the triangle. The third angle would be represented by " 5x - 18 "

Now the equation would look like this

x + 5x + (5x-18) = 180  combine the like terms together

By combining the like terms it would be

11x - 18 = 180     now add 18 on both sides

11x = 198   divide 11 from both sides

x = 18     Now, 18 is the angle measure of the smallest angle

Now we have to find the angles measure of the other angles

To find the largest angle the equation is

5 X 18 = 90 which is the measure of the largest angle

To find the third angle the equation would look like

5 X 18 - 18 = 72 which is the measure of the third angle

Smallest angle = 18 degrees

Largest angle = 90 degrees

Third angle = 72 degrees

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Let x be smallest angle, 5x be largest angle, and 5x-18 be the third angle.

The sum of angles in the triangle is 180 degrees, so add up all the angle given and equal it to 180

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

11x-18=180

11x=198

x= 18

Thus, smallest angle is 18 degrees, biggest angle is 18*5=90 degrees and the third angle is 90-18= 72 degrees.

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Let x = small angle

Let 5x = larger angle

Let 5x-18 = third angle

x+5x+5x-18=180

11x-18=180

11x=198

x=18

Small angle = 18

Large = 90

Third = 72

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