Question

Please help me with this math problem!

Answer 1

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 $(2x + 7)$ and $(3x - 7)$ are equal.

With this information, we can solve for $x$:

$2x + 7 = 3x - 7$

$2x - 3x = -7 - 7$

$-x = -14$

$x = 14$

Now that we know $x$, we can determine what the actual value of these angles are:

$2x + 7$

$2(14) + 7$

$28 + 7$

$35$

or

$3x - 7$

$3(14) - 7$

$42 - 7$

$35$

Now, we see that the top line of the two parallel lines cuts the right side of the triangle into two angles, $(2x + 7)$ and $(12y + 1)$. Since it's cutting a straight line into two angles, we know that the same of these angles must be $180$°. We already solved for the top angle and found that it is $35$°, so that means the bottom angle is $145$°. With this, we can solve for $y$:

$12y + 1 = 145$

$12y = 144$

$y = 12$

Therefore, the answer is $x = 14, y = 12$