Question

Solve to find x and y in the diagram.

Answer 1

Considering the given information in the question, the value of x is $12^{o}$, and that of y is $7.5^{o}$.

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,

$(5x+4y)^{o}$ = $(12y)^{o}$

$5x^{o}$ = $12y^{o}$ - $4y^{o}$

$5x^{o}$ = $8y^{o}$............ 1

Also given that the top right angle at the second intersection is a right angle, then;

    $12y^{o}$ + $90^{o}$ = $180^{o}$ (sum of angles on a straight line)

This implies that;

    $12y^{o}$ = $180^{o}$ -    $90^{o}$

       $12y^{o}$  =     $90^{o}$

So that,

y = $\frac{90}{12}$

y = $7.5^{o}$

Thus substituting the value of y in equation 1, we have;

$5x^{o}$ = $8y^{o}$........ 1

     = 8(7.5)

5x = 60

x = $\frac{60}{5}$

x = $12^{o}$

Therefore, x = $12^{o}$ and y = $7.5^{o}$

For more clarification on a transversal of two parallel lines, check: brainly.com/question/1751268

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