We first need to put all three angles in math expressions that we can work with. We start by finding what they have in common:
"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 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle."
So, we know that a triangle has 3 angles, and that these angles add up to 180 degrees. Since two of the angles were talked about in terms of the smallest angle, we will call the smallest angle "x."
x = smallest angle
3x = another angle
x + 45 = last angle
We then add them all together and solve for x:
x + 3x + x + 45 = 180
5x + 45 = 180
5x = 135
x = 27
Almost there! The question asked for what the largest angle is. Now we have to plug 27 back in and find out:
x = 27 = smallest angle
3x = 3(27) = 81
x + 45 = 27 + 45 = 72
To double check: 27 + 81 + 72 = 180.
The largest angle is 81 degrees.