TITLE: Determine missing angle in polygon
QUESTION [0 upvotes]: 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).

REPLY [2 votes]: 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?
{"set_name": "stack_exchange", "score": 0, "question_id": 688004}