1. A segment that joins two nonconsecutive vertices.
Drawing the diagonals from one vertex divides the polynomial into (n - 2) triangles, where n is the number of sides of the polygon.
360°

2. 6 6
720°
720°

3. ° °
nonagon

4. 71° ° ° °
318° °
42°

5. Sum = (n - 2)180
Sum = (10 - 2)180
Sum = (8)180
Sum = 1440°
Sum = (n - 2)180
1620 = (n - 2)180
9 = n - 2
11 = n
11-gon (hendecagon or undecagon)
Sum = (n - 2)180
Sum = (5 - 2)180
Sum = (3)180
Sum = 540°
m∠K + m∠L + m∠M + m∠N + m∠J = Sum
x + x + 109° + 105° + 68° = 540°
2x + 282° = 540°
2x = 258°
x = 129°
m∠K = m∠L = 129°

6. 360°
360°
89° x ° °
° °
3x = 186°
62°

7.
2340°
mInt∠ =
(n - 2)180
_________ n 15
2340° ° °
156° °
360° °
mExt∠ =
360
____ n
24°

8. m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360°
66° + 77° + 82° + 62° + x = 360°
287° + x = 360°
x = 73°
mInt∠ =
(n - 2)180
_________ n
(9 - 2)180 9
mInt∠ = 140°
mExt∠ =
360°
____ n 9
mExt∠ = 40