Question 134132: Hello,
I am in need of some help with an algebra problem example...I need to figure out this example to use to do my other homework. I thought maybe you could help me find the solution, and help me to understand the steps to finding the solution? I am not good with angles at all. Your help would be very much appreciated.:)
The sum of the interior angles of all triangles is 180º. If one angle is 3 times the smallest and the third angle is 30 more than the smallest angle, find the size of the smallest angle. Be sure to include all work.
Thank you,
Mrs. Gibson
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! First of all, this is a geometry problem not pure algebra. Secondly, you are good in terms of angles. You probably have not been taught correctly.
I will try to rectify this problem by making this question clear.
Your question:
The sum of the interior angles of all triangles is 180º. If one angle is 3 times the smallest and the third angle is 30 more than the smallest angle, find the size of the smallest angle. Be sure to include all work.
"one angle is three times the smaller" is written 3x. We don't know what the smaller angle measures. I will use x to represent the smallest angle. You can use ANY LETTER of choice to represent the angle.
The smaller angle is x.
"...the third angle is 30 more than the smaller angle" is written x + 30.
The words "more than" indicates addition. We know the smaller angle is x and so, 30 more than x = x + 30. Is this clear?
At the start of the question it is written:
"The sum of the interior angles of all triangles is 180º." This is worldwide triangle fact. Of course, this fact applies to plane geometry, which is what you are doing.
We now have everything we need to find x...our smallest angle.
x + 3x + x + 30 = 180º
5x + 30 = 180º
5x = 180º - 30
5x = 150
x = 150/5
x = 30
What is the measure of the smallest angle in this triangle?
It is 30 degrees?
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