Question

The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle x. What are the measures of the angles? The measure of angle x is 122. 5 degrees. The measure of angle y is 57. 5 degrees. The measure of angle x is 115 degrees. The measure of angle y is 65 degrees. The measure of angle x is 57. 5 degrees. The measure of angle y is 122. 5 degrees. The measure of angle x is 65 degrees. The measure of angle y is 115 degrees.

Answer 1

Supplementary angles are two angle whose sum is equal to the 180 degrees. Supplementary angles forms linear together. The measure of angle x is 122. 5 degrees and  the measure of angle y is 57. 5 degrees. The option 1 is the correct option.

Given Information-

Measures of two supplementary angles is 180 degrees.

The measure of angle y is 65 degrees less than the measure of angle x.

Supplementary angles-

Supplementary angles are two angle whose sum is equal to the 180 degrees. Supplementary angles forms linear together.

As in the given question two supplementary angles x and y are given and the sum of both the angles are equal to the 180 degrees. Thus,

$x+y=180\;\;\;\;\;\;\;\;\;\ .......1$

The measure of angle y is 65 degrees less than the measure of angle x. Thus,

$y=x-65\;\;\;\;\;\;\;\;\;\ .......2$

Put this value of the angle y in equation 1, we get,

$\begin{aligned}x+(x-65) &=180\\2x &=180+65\\2x &=245\\x &=\dfrac{245}{2} \\x &=122.5\\\end$

Thus the measure of angle x is 122. 5 degrees.

Put this value in the equation 2 to get the value of the angle y.

$y=122.5-65\\y=57.5$

Thus, the measure of angle y is 57. 5 degrees.

Hence the measure of angle x is 122. 5 degrees and  the measure of angle y is 57. 5 degrees. The option 1 is the correct option.

Learn more about the supplementary angles here;

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