Final answer:
The equation to find both angles is x + y = 180, where y = x - 30.
Step-by-step explanation:
To find the equation to find both angles, we can represent the larger angle as x and the smaller angle as y. Given that the angles are supplementary and the smaller angle is 30 degrees less than the larger one, we can set up the equation x + y = 180 and y = x - 30. Simplifying the equation, we get x + (x - 30) = 180. Combining like terms, we have 2x - 30 = 180. Adding 30 to both sides, we get 2x = 210. Finally, dividing both sides by 2, we find x = 105. Substituting this value back into the equation y = x - 30, we have y = 105 - 30, which gives us y = 75.