The variables x and y have their values to be 50 degrees and 20 degrees, respectively
<h3>How to determine the values of the variables?</h3>
The triangle, the lines and the angles represent the given parameters
On the triangle, we have the following corresponding angles
Angle 5y and angle 2x
Corresponding angles have equal measure
So, we have the following representation
2x = 5y
Divide both sides by 2
x = 2.5y
The angle on a straight line is 180 degrees
So, we have the following representation
5y + 180 - 2x - (x - y) + 30 = 180
Remove the bracket
So, we have
5y + 180 - 2x - x + y + 30 = 180
Subtract 180 from both sides
This gives
5y - 2x - x + y + 30 = 0
Substitute x = 2.5y in 5y - 2x - x + y + 30 = 0
5y - 2(2.5y) - 2.5y + y + 30 = 0
So, we have
5y - 5y - 2.5y + y + 30 = 0
Evaluate the like terms
1.5y = 30
Divide both sides by 1.5
y = 20
Recall that x = 2.5y
So, we have
x = 2.5 * 20
Evaluate
x =50
Hence, the measures of the variables are x = 50 and y = 20
Read more about angles at
brainly.com/question/7620723
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