Answer
The measure of the interior angle at vertex N is $~190^{\circ}$
Work Step by Step
We can find the value of $y$ by considering the sum of all six interior angles:
$y+y+y+y+2(y+10)+2(y+10) = (6-2)~\cdot 180^{\circ}$
$8y+40 = (4)~\cdot 180^{\circ}$
$8y+40 = 720^{\circ}$
$8y = 680^{\circ}$
$y = 85^{\circ}$
We can find the measure of the interior angle at vertex N:
$2(y+10) = (2) \cdot (85^{\circ}+10^{\circ}) = 190^{\circ}$
