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The sum of three angles of a triangle is 180 degrees. The largest angle of the triangle...
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!
5 Answers | add yours
High School Teacher
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
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)
Posted by lynn30k on November 19, 2008 at 10:06 AM (Answer #1)
Middle School Teacher
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?
Posted by cburr on November 19, 2008 at 10:54 AM (Answer #2)
x= 18 degrees. More info I think here is a best link for you.
Posted by jones123 on November 19, 2008 at 9:07 PM (Answer #3)
Let x = small angle
Let 5x = larger angle
Let 5x-18 = third angle
Small angle = 18
Large = 90
Third = 72
Posted by dracomath on December 28, 2008 at 1:19 AM (Answer #4)
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
Thus, smallest angle is 18 degrees, biggest angle is 18*5=90 degrees and the third angle is 90-18= 72 degrees.
Posted by revolution on July 17, 2010 at 6:35 PM (Answer #5)
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