Question

1 week streak level 5
note: angles not necessarily drawn to scale.
x = □□

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle with measure $30^{\circ}$ and the angle adjacent to $x^{\circ}$ are vertical - angles, so the angle adjacent to $x^{\circ}$ is $30^{\circ}$.

Step2: Use the fact that $AB\perp CD$

Since $AB$ is perpendicular to $CD$, the angle formed at $G$ is $90^{\circ}$. We know that the sum of the angle adjacent to $x^{\circ}$ and $x^{\circ}$ is $90^{\circ}$. Let the angle adjacent to $x^{\circ}$ be $\alpha = 30^{\circ}$. Then $x+\alpha=90^{\circ}$.

Step3: Solve for $x$

Substitute $\alpha = 30^{\circ}$ into the equation $x + \alpha=90^{\circ}$. We get $x=90 - 30$.
$x = 60$

Answer:

$60$