OK, so when you have a regular n-gon, you can figure out each angle in it using this formula: [(n-2)180]/n. In this case, 7*180/9 = 140, so we know each angle in the polygon is 140°.

I couldn’t draw this quickly on the computer I’m on, so I found a good n-gon picture to mark up from Wikipedia. 🙂 Please forgive the kinda sloppy graphics below once I start marking up the figure.

By László Németh – Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=27295121

Now here’s what we care about:

We can get at the measure of ACE by considering that triangles ABC and CDE are isoscelese (because this is a regular polygon), and that angles B and D are 140°. Therefore, the small angles in those triangles must all be 20° (because triangle angles always add to 180°).

We know angle BCD is also 140°, and we’re taking 20° from it on either side. Therefore, the measure of angle ACE is 140° – 20° – 20° = 100°.

from Tumblr https://ift.tt/2yC56Ku