Answer:
Solve for x: x + 128 = 180, x = 52°
Solve for y: x + y = 90 or 52 + y = 90, y = 38°
Step-by-step explanation:
In order to solve for the measures of ∠x and ∠y, you first need to remember that angles that are complementary add up to 90° and angles that are supplementary add up to 180°. So, in order to solve for 'x', which is supplementary to a 128° angle, we can set up an equation where the sum of ∠x and 128° = 180°:
x + 128 = 180, subtract 128 from both sides: x + 128 - 128 = 180 - 128, x = 52°
Knowing that ∠x + ∠y = 90° and now that ∠x = 52°, we can set up the second equation:
52 + y = 90, subtract 52 from both sides: 52 + y - 52 = 90 - 52 or y = 38°
