The Triangle Angle-Sum theorem tells us that the angles of a triangle add up to 180, no matter what kind of triangle we have. Now we just have to figure out how to express the sides in terms of an unknown x. It looks like all 3 angles are based on the measure of the first. We will call the first angle x. The next one is 4 times the first, so the largest is 4x. The third is 30 less than the first, so the third is x - 30. We add those and set them equal to 180. x+4x+x-30=180. Combining like terms we have 6x = 210, and x = 35. The smallest angle is 35. The largest is 4(35) = 140. The third is 35-30 = 5. And there you go!
