Considering the given information in the question, the value of x is [tex]12^{o}[/tex], and that of y is [tex]7.5^{o}[/tex].
A transversal is a line that cuts through two given parallel lines. Thus it intersects each parallel line at a point, forming four angles each.
From the given information in the question, it can be inferred that:
the given bottom right angle of the first intersection and the bottom right angle with the second intersection are congruent (corresponding angle property).
So that,
[tex](5x+4y)^{o}[/tex] = [tex](12y)^{o}[/tex]
[tex]5x^{o}[/tex] = [tex]12y^{o}[/tex] - [tex]4y^{o}[/tex]
[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]............ 1
Also given that the top right angle at the second intersection is a right angle, then;
[tex]12y^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)
This implies that;
[tex]12y^{o}[/tex] = [tex]180^{o}[/tex] - [tex]90^{o}[/tex]
[tex]12y^{o}[/tex] = [tex]90^{o}[/tex]
So that,
y = [tex]\frac{90}{12}[/tex]
y = [tex]7.5^{o}[/tex]
Thus substituting the value of y in equation 1, we have;
[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]........ 1
= 8(7.5)
5x = 60
x = [tex]\frac{60}{5}[/tex]
x = [tex]12^{o}[/tex]
Therefore, x = [tex]12^{o}[/tex] and y = [tex]7.5^{o}[/tex]
For more clarification on a transversal of two parallel lines, check: https://brainly.com/question/1751268
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