Question

what if? as shown, part of the extending arm of a desk lamp is a parallelogram. the angles of the parallelogram change as the lamp is raised and lowered. find $m\angle c$ when $m\angle d$ is twice the measure of $\angle c$.
$m\angle c = \square^\circ$

Explanation:

Step1: Define variables for angles

Let $m\angle C = x$, then $m\angle D = 2x$.

Step2: Use parallelogram angle property

Consecutive angles in a parallelogram are supplementary, so:
$$x + 2x = 180^\circ$$

Step3: Solve for $x$

Combine like terms and isolate $x$:
$$3x = 180^\circ$$
$$x = \frac{180^\circ}{3} = 60^\circ$$

Answer:

$60$