# Determine missing angle in polygon

I'm trying to figure out this question:

Determine the measure of angle a


I'm guessing $a=96\unicode{0186}$ using the following work:

$$a = 180 - 84 = 96$$

I also measured the angles in the polygon and found that $a$ was ~$90\unicode{0186}$. We're learning about Properties of Angles and Triangles (which includes interior & exterior opposite angles, corresponding angles, etc) but I can't see how to figure out the angle using that? Any ideas?

(Please ignore my bad drawing, The bottom right corner should've gone out a bit further so a straight line can be drawn from the top right all the way down).

• Hint: the sum of the interior angles in a hexagon is 720°. – hmakholm left over Monica Feb 24 '14 at 2:44
• I edited your question to remove the "algebraic-geometry" tag and replace it with the "euclidean-geometry" one. Algebraic geometry actually means something completely different from you probably assumed it means. :) – David H Feb 24 '14 at 3:49

Hint: label the points on the polygon $A,B,C,D,E,F$ such that $\angle ABC = 36^{\circ}$ and $\angle BCD = (360-84)^{\circ} = 276^{\circ}$. For any polygon with $n$ sides, the sum of the internal angles must be $(180(n-2))^{\circ} = (36 + 276 + 4a)^{\circ}$. Can you figure out why, and can you take it from here?
• So $a = 102\unicode{0186}$? – ub3rst4r Feb 24 '14 at 2:55