Question

quadrilateral defg is an isosceles trapezoid and ( mangle g = 7u + 20^circ ). what is the value of ( u )?

Explanation:

Step1: Identify consecutive angles property

In an isosceles trapezoid, consecutive angles between the bases are supplementary (sum to $180^\circ$). So $\angle F + \angle G = 180^\circ$.

Step2: Substitute given values

Substitute $m\angle F = 118^\circ$ and $m\angle G = 7u + 20^\circ$:
$118 + (7u + 20) = 180$

Step3: Simplify left side

Combine constant terms:
$7u + 138 = 180$

Step4: Isolate the variable term

Subtract 138 from both sides:
$7u = 180 - 138$
$7u = 42$

Step5: Solve for u

Divide both sides by 7:
$u = \frac{42}{7}$

Answer:

$u = 6$