One angle of a triangle is 50 degrees greater than the smallest angle, and the third angle is 10 degrees less than twice the smallest angle. find the measures of the three angles.

By the Triangle Angle-Sum theorem, the angles of a triangle add up to 180, no matter what kind of a triangle it is.  Now we just have to determine how to identify each angle according to the info we have.  It looks like all 3 angles are dependent upon the measure of the smallest angle, so we will call the smallest angle x.  The second angle is 50 degrees more than the smallest, so the second angle is x + 50.  The third angle is 10 degrees less than 2 times the smallest angle, so the third angle is 2x-10.  We will add all those together and set them equal to 180.  x+x+50+2x-10=180.  Combining like terms we have 4x+40=180, and 4x = 140.  x = 35.  So the smallest angle measures 35.  The second one is 50 more, so the second one is 85.  The third one is 10 less than twice the smallest, so the third angle is 60.  Add those results together and make sure they come to 180.  They do!