Answer:
nonagon: 140°
100-gon: 176.4°
Step-by-step explanation:
A regular polygon is one that has all sides the same length and all internal angles the same measure. A "nonagon" has nine (9) sides. An image of one is attached. There are some interesting relationships among the angles shown.
The figure can be divided into 9 congruent triangles. Each has a vertex at the center of the figure, and the other two vertices are each end of one side. The central angle (40°) is the supplement of the interior angle at each vertex of the nonagon (140°). Obviously, the central angles sum to 360° (one full circle), so each one has a measure that is 360° divided by the number of sides:
360°/9 = 40°
So, we can figure the interior angle (at the vertex) by subtracting from 180° the value of 360° divided by the number of sides.
For the 100-gon, with 100 sides, the interior angle will be ...
180° -360°/100 = 180° -3.6° = 176.4°
