## Elementary Geometry for College Students (7th Edition)

The measure of the interior angle at vertex N is $~190^{\circ}$
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: $2(y+10) = (2) \cdot (85^{\circ}+10^{\circ}) = 190^{\circ}$