ANGLES X AND Y ARE SUPPLEMENTARY ,AND THE MEASURE OF ANGLES X IS 24 DEGREES GREATER THAN THE MEASURE OF ANGLE Y. FIND THE ANGLE MEASURES.

Y + Y + 24 = 180

2Y = 156

Y = 78

http://www.mathsisfun.com/geometry/supplementary-angles.html

A.45

B.60
C.120
D.135

Let's assume that the measure of angle Y is 'y' degrees.

According to the given information, angle X is 24 degrees greater than angle Y. So, the measure of angle X is 'y + 24' degrees.

Since angles X and Y are supplementary, their sum is 180 degrees.

This can be written as:
X + Y = 180

Substituting the values of angles X and Y, we have:
(y + 24) + y = 180

Combining like terms, we get:
2y + 24 = 180

Subtracting 24 from both sides, we obtain:
2y = 156

Dividing both sides by 2, we find:
y = 78

Now, we can substitute the value of y back into the equation to determine the measure of angle X:
X = y + 24 = 78 + 24 = 102

Therefore, the measure of angle X is 102 degrees, and the measure of angle Y is 78 degrees.

To find the angle measures, let's first set up an equation based on the given information.

Let the measure of angle Y be represented by "y" degrees. Since angle X is 24 degrees greater than angle Y, the measure of angle X would be "y + 24" degrees.

Since angles X and Y are supplementary, their sum is equal to 180 degrees. Therefore, we can write the equation as follows:

x + y = 180

Substituting the values we determined:

(y + 24) + y = 180

Now, we can solve for "y" by rearranging the equation:

2y + 24 = 180

Subtracting 24 from both sides:

2y = 156

Dividing both sides by 2:

y = 78

Thus, the measure of angle Y is 78 degrees.

To find the measure of angle X, we substitute the value of "y" back into our equation:

x = y + 24
x = 78 + 24
x = 102

Therefore, the measure of angle X is 102 degrees.