Question

The sum of the measures of angles X and Y is 180 degrees. The measure of angle X is 24 degrees greater than the measure of angle Y. Define the variables, and write equations for this situation.

Answer 1

Answer:

The measure of angle x is 102 degrees and the measure of angle y is 78 degrees

Step-by-step explanation:

we know that

$x+y=180\°$ -----> equation A (supplementary angles)

$x=y+24\°$ ----> equation B

Solve the system by substitution

substitute equation B in equation A

$y+24\°+y=180\°$

Solve for y

$2y+24\°=180\°$

$2y=180\°-24\°$

$2y=156\°$

$y=78\°$

Find the measure of angle x

$x=102\°=$

therefore

The measure of angle x is 102 degrees and the measure of angle y is 78 degrees