A triangle has angle measures that are related as follows: -The largest angle is 12 times the smallest angle -The middle angle is 5 times the...

The total number of degrees in any triangle is 180. There are several ways to set up an equation to answer this question, but the easiest way is to let the measure of the smallest angle of the three equal to x. We are told in the problem that the largest angle is 12 times the smallest, and the middle angle is 5 times the smallest. Therefore, the largest angle is 12x, and the middle is 5x. Since we know the sum of the three angles is 180 degrees, our equation becomes

12x + 5X + x = 180

Combining like terms, our equation simplifies to

18x = 180

Dividing each side by 18 in order to get x by itself, we get

x=10

Therefore, the smallest angle is 10 degrees, the medium in size is 50 degrees, and the largest is 120 degrees. We can check our work by adding these three angle measures; the result is 180 degrees, so our answer checks.