Question

find the value of w that makes quadrilateral defg a parallelogram.
(there is a diagram of quadrilateral defg with angle at f labeled 2w, angle at d labeled w + 50°, and angles at g and e marked with red arcs indicating they are equal.)
w = °

Explanation:

Step1: Use parallelogram angle property

In a parallelogram, consecutive angles are supplementary, so $\angle F + \angle D = 180^\circ$. Substitute the given angles:
$2w + (w + 59^\circ) = 180^\circ$

Step2: Simplify the equation

Combine like terms:
$3w + 59^\circ = 180^\circ$

Step3: Isolate the variable term

Subtract $59^\circ$ from both sides:
$3w = 180^\circ - 59^\circ = 121^\circ$

Step4: Solve for $w$

Divide both sides by 3:
$w = \frac{121^\circ}{3} \approx 40.33^\circ$

Answer:

$w = \frac{121}{3}$ or approximately $40.33^\circ$