Supplementary angles are two angle whose sum is equal to the 180 degrees. Supplementary angles forms linear together. The measure of angle <em>x</em> is 122. 5 degrees and the measure of angle <em>y</em> is 57. 5 degrees. The option 1 is the correct option.
<h3>Given Information-</h3>
Measures of two supplementary angles is 180 degrees.
The measure of angle <em>y</em> is 65 degrees less than the measure of angle <em>x.</em>
<h3>Supplementary angles-</h3>
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 <em>x </em>and <em>y </em>are given and the sum of both the angles are equal to the 180 degrees. Thus,
![x+y=180\;\;\;\;\;\;\;\;\;\ .......1](https://tex.z-dn.net/?f=x%2By%3D180%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%20.......1)
The measure of angle <em>y</em> is 65 degrees less than the measure of angle <em>x. </em>Thus,
![y=x-65\;\;\;\;\;\;\;\;\;\ .......2](https://tex.z-dn.net/?f=y%3Dx-65%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%20.......2)
Put this value of the angle <em>y</em> in equation 1, we get,
![\begin{aligned}x+(x-65) &=180\\2x &=180+65\\2x &=245\\x &=\dfrac{245}{2} \\x &=122.5\\\end](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx%2B%28x-65%29%20%26%3D180%5C%5C2x%20%26%3D180%2B65%5C%5C2x%20%26%3D245%5C%5Cx%20%26%3D%5Cdfrac%7B245%7D%7B2%7D%20%5C%5Cx%20%26%3D122.5%5C%5C%5Cend)
Thus the measure of angle <em>x</em> is 122. 5 degrees.
Put this value in the equation 2 to get the value of the angle <em>y.</em>
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Thus, the measure of angle <em>y</em> is 57. 5 degrees.
Hence the measure of angle <em>x</em> is 122. 5 degrees and the measure of angle <em>y</em> is 57. 5 degrees. The option 1 is the correct option.
Learn more about the supplementary angles here;
brainly.com/question/3027144