Question

I need help with this problem. ​

Answer 1

Answer:

$x=6,\\m\angle 1=18^{\circ}$

Step-by-step explanation:

Since the problem denotes the figure as a parallelogram, $\overline{AB}$ is parallel to $\overline{DC}$. Therefore, angles 1 and 2 are equal (from corresponding angles and vertical angles).

Therefore, we have the following equation:

$m\angle 1=m\angle 2,\\x+12=6x-18,\\30=5x,\\x=\boxed{6}$

Substituting $x=6$:

$m\angle 1=x+12=6+12=\boxed{18^{\circ}}$