one angle of an obtuse triangle measures four times the first angle. the third angle measures 30° less than the first angle. what are the degree measures of the three angles? the smallest angle is ° the largest angle is ° the third angle is °

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!

Iwould say they are complementary because that’s the division of a 90 degree angle and it’s split between the middle of them

The operation is suck a c@ck? !