#### Answer

The measure of the reflex angle at vertex E is $~216^{\circ}$

#### Work Step by Step

We can find the value of $x$ by considering the sum of all five interior angles:
$x+x+2x+2x+4x = (5-2)~\cdot 180^{\circ}$
$10x = (3)~\cdot 180^{\circ}$
$x = 54^{\circ}$
We can find the measure of the reflex angle:
$4x = (4) \cdot (54^{\circ}) = 216^{\circ}$