Question

Give the convex pentagon, what are the values for x and y?

Answer 1

Now.. if you check the picture below

notice that, "x" and "y" are just "supplementary" angles

so.. what the dickens is "x" anyway?

well, "x" is an internal angle to the pentagon

and $\bf \textit{sum of all interior angles in a polygon}\\\\ 180(n-2)\qquad n=\textit{number of sides}$

so.. this polygon is a pentagon, or PENTA=5, 5 sides
so all internal angles add up to 180(5-2) or 180*3 = 540

now, check the angle on the bottom-left-corner, is a right-angle

so... you already have 4 angles given inside

so   x + 80 + 160 + 100 + 90 = 540

solve for "x"

what about "y"?   well, y = 180 - x