Question

Two angles whose measures have a sum of 90° are called complementary angles. Let x and y represent the measures of complementary angles. Use this information and the equation given in the problem to find the measure of each angle. x = 8y The measure of x is ____ and the measure of y is ____.

a) The measure of x is 64° and the measure of y is 8°

b) The measure of x is 8° and the measure of y is 64°

c) The measure of x is 72° and the measure of y is 18°

d) The measure of x is 18° and the measure of y is 72°

Answer 1

To find the measure of x and y, we can set up equations using the given information. By substituting the value of x into the equation x + y = 90°, we can solve for y. Plugging the value of y back into the second equation gives us the measure of x. The measure of x is 80° and the measure of y is 10°.

Step-by-step explanation:

To find the measure of each angle, we need to set up an equation using the information given. Since the angles are complementary, their measures add up to 90°. So, we have the equation x + y = 90°. We also have the equation x = 8y.

Substitute the value of x from the second equation into the first equation. x = 8y, so the first equation becomes 8y + y = 90°. Combine like terms and solve for y. 9y = 90°, y = 10°.

Plug the value of y back into the second equation to find x. x = 8(10°), x = 80°.

Therefore, the measure of x is 80° and the measure of y is 10°.