One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 40 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
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Bon, please read my explanation carefully so that you can do similar problems by yourself next time. There are MANY similar problems to this in mathematics!
The way this problem allows us to express the measure of each of the three angles of the triangle in terms of the measure of the smallest angle.
Let's call S to represent the measure of the smallest angle. That measure is unknown to us at this point. The first angle described, let's call its measure A, has a measure of 3S.
The measure of the third angle, let's call its measure B, is described as 40 degrees more than the smallest angle, so B = S + 40.
Here's what we have:
S: measure of smallest angle in degrees
A = 3S
B = S + 40
The information we bring to the problem is that the three angles of every triangle add up to 180 degrees. Thus:
S + A + B = 180
Let's substitute the equivalent values for A and B into the equation to get:
S + 3S + (S + 40) = 180
Let's simplify this to get:
S + 3S + S + 40 = 180
Let's combine like terms to get:
5S + 40 = 180
Let's subtract 40 from each side of the equal sign to isolate the unknown on one side:
5S + 40 – 40 = 180 – 40
5S = 140
Now we find S by dividing each side of the equation by 5:
S = 28
We know now that the SMALLEST angle measures 28 degrees.
A is three times that or (3)(28) or 84 degrees.
B is 40 plus S or 40 + 28 or 68 degrees.
What is the measure of the largest angle???
You got it!!!
