Step-by-step explanation:
Since the two lines running left to right are parallel, and cut into the right side of the triangle, the angles [tex](2x + 7)[/tex] and [tex](3x - 7)[/tex] are equal.
With this information, we can solve for [tex]x[/tex]:
[tex]2x + 7 = 3x - 7[/tex]
[tex]2x - 3x = -7 - 7[/tex]
[tex]-x = -14[/tex]
[tex]x = 14[/tex]
Now that we know [tex]x[/tex], we can determine what the actual value of these angles are:
[tex]2x + 7[/tex]
[tex]2(14) + 7[/tex]
[tex]28 + 7[/tex]
[tex]35[/tex]
or
[tex]3x - 7[/tex]
[tex]3(14) - 7[/tex]
[tex]42 - 7[/tex]
[tex]35[/tex]
Now, we see that the top line of the two parallel lines cuts the right side of the triangle into two angles, [tex](2x + 7)[/tex] and [tex](12y + 1)[/tex]. Since it's cutting a straight line into two angles, we know that the same of these angles must be [tex]180[/tex]°. We already solved for the top angle and found that it is [tex]35[/tex]°, so that means the bottom angle is [tex]145[/tex]°. With this, we can solve for [tex]y[/tex]:
[tex]12y + 1 = 145[/tex]
[tex]12y = 144[/tex]
[tex]y = 12[/tex]
Therefore, the answer is [tex]x = 14, y = 12[/tex]
