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.