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

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

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