Question

quadrilateral defg is an isosceles trapezoid and ( mangle g = 5v - 42^circ ). what is the value of ( v )?

( v = square^circ )

Explanation:

Step1: Identify consecutive angles property

In an isosceles trapezoid, consecutive angles between the bases are supplementary. So $m\angle G + m\angle D = 180^\circ$.

Step2: Substitute given values

Substitute $m\angle G = 5v - 42^\circ$ and $m\angle D = 128^\circ$ into the equation:
$5v - 42 + 128 = 180$

Step3: Simplify the left side

Combine constant terms:
$5v + 86 = 180$

Step4: Isolate the variable term

Subtract 86 from both sides:
$5v = 180 - 86$
$5v = 94$

Step5: Solve for v

Divide both sides by 5:
$v = \frac{94}{5} = 18.8$

Answer:

$v = 18.8$