Question

Angle x and y are complementary. Angle X is supplementary to a 128° angle. What are the measures of angle X and angle Y? Write an equation to solve for X first. Then find the measure of angle Y

Answer 1

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°