Question

quadrilateral defg is an isosceles trapezoid and m∠g = w + 72°. what is the value of w? w =

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, base - angles are equal. So, $\angle D=\angle G$.

Step2: Set up the equation

Since $m\angle D = 127^{\circ}$ and $m\angle G=w + 72^{\circ}$, we have the equation $w + 72^{\circ}=127^{\circ}$.

Step3: Solve for w

Subtract $72^{\circ}$ from both sides of the equation: $w=127^{\circ}-72^{\circ}$.
$w = 55^{\circ}$

Answer:

$55$