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
![](https://i0.wp.com/66.media.tumblr.com/c3ad8a16f1123e3a3eaae96383538d44/98555b8a3bc10b4c-6e/s640x960/195897884145e2b6a193db144dbe04fca9d227c5.png?w=852&ssl=1)
Now here’s what we care about:
![](https://i0.wp.com/66.media.tumblr.com/8d29b85b57609efda968698b66c28359/98555b8a3bc10b4c-ec/s640x960/003fcf4a7d2c0cb82ca33e41df5b110baa4e81a2.png?w=852&ssl=1)
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°).
![](https://i0.wp.com/66.media.tumblr.com/9f867494673d8b45726909647f7b8647/98555b8a3bc10b4c-47/s640x960/c811f76c04562df9f7c65a972c1bf11dcb699e83.png?w=852&ssl=1)
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°.
![](https://i0.wp.com/66.media.tumblr.com/adae25b2a1524083bc2de928f6e20eb9/98555b8a3bc10b4c-cc/s640x960/440b61e9f67bab00d4fa3e338edc939e39c73de2.png?w=852&ssl=1)
from Tumblr https://ift.tt/2yC56Ku