Two angles are supplementary. The definition of supplementary is that the two angles have to add up to be 180°. If it had said complementary, then the two angles would add up to be 90°. Then it says 1 angle is 5 less than four times the other. So one angle traditionally in mathematics is means equals 5 less. So we're going to take five away from something, then four times the other, so four times the other five, less than four times the other. Find the measure of the angles. So now if we have X + y equal 180 and X equaling four y -, 5, we're going to take out this X by our substitution and we're going to stick in four y -, 5. So when we solve this, we're going to combine our like terms, five y -, 5 equaling 180. We're going to add five to each side SO5Y equal 185. So Y is going to equal 5 into 185 is going to give me 37 because 5 into 18 is three times for a 15, leaving us a three with the following number of 55 into 35 is 7. So we know if Y is 37 then we can find X and we can find it from either of the two equations X + 37 equal 180. When we subtract, we're going to get X equaling 143. Now to check it. Those two numbers better work in both of them. So 143 + 37 is 180. Does 143 really equal 4 * 37 - 5? Well, 4 * 37 we get an 8 and carry a 212 with the two that we carried. So 148 - 5 S 143 does equal this. So the two angles are a 143° and 37°.