Question

in the figure below, g || m.
find the values of x and y.
x =
y =
(there is a diagram with parallel lines g and m, a transversal h, angles 67°, x°, and (3y + 1)°)

Explanation:

Step1: Solve for $x$ (vertical angles)

Vertical angles are equal, so $x = 67$.

Step2: Solve for $y$ (supplementary angles)

$x$ and $3y+1$ are supplementary:
$$67 + (3y + 1) = 180$$
Simplify:
$$3y + 68 = 180$$
$$3y = 180 - 68$$
$$3y = 112$$
$$y = \frac{112}{3} \approx 37.33$$

Answer:

$x = 67$
$y = \frac{112}{3}$ (or approximately $37.33$)