Question

quadrilateral defg is a rhombus and ( mangle cde = w + 12^circ ). what is the value of ( w )?

Explanation:

Step1: Use rhombus diagonal property

In a rhombus, diagonals bisect the interior angles, so $m\angle CDE = m\angle DGC = 29^\circ$.

Step2: Set up equation for $w$

Equate the angle expression to $29^\circ$:
$w + 12^\circ = 29^\circ$

Step3: Solve for $w$

Subtract $12^\circ$ from both sides:
$w = 29^\circ - 12^\circ$

Answer:

$17$