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.
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 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,
[tex]x+y=180\;\;\;\;\;\;\;\;\;\ .......1[/tex]
The measure of angle y is 65 degrees less than the measure of angle x. Thus,
[tex]y=x-65\;\;\;\;\;\;\;\;\;\ .......2[/tex]
Put this value of the angle y in equation 1, we get,
[tex]\begin{aligned}x+(x-65) &=180\\2x &=180+65\\2x &=245\\x &=\dfrac{245}{2} \\x &=122.5\\\end[/tex]
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.
[tex]y=122.5-65\\y=57.5[/tex]
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.
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