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).

  • $\begingroup$ Hint: the sum of the interior angles in a hexagon is 720°. $\endgroup$ – hmakholm left over Monica Feb 24 '14 at 2:44
  • $\begingroup$ 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. :) $\endgroup$ – 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?

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  • $\begingroup$ So $a = 102\unicode{0186}$? $\endgroup$ – ub3rst4r Feb 24 '14 at 2:55

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