Step-by-step explanation:
An exterior angle of a polygon is an angle outside a polygon formed by one of its sides and the extension of an adjacent side. As shown in the figure below, for example, illustrates the exterior angles (red) of a regular convex pentagon (5-sided polygon).
The exterior angle sum theorem states that if a polygon is convex, the sum of its exterior angle will always be 360°. Therefore, the magnitude of each exterior angle of a n-sided polygon can be evaluated using the formula
[tex]\text{Exterior angle} \ = \ \displaystyle\frac{360}{n}[/tex].
Hence, for a convex 21 sided-polygon (henicosagon), each exterior angle will be
[tex]\text{Exterior angle} \ = \ \displaystyle\frac{360^{\circ}}{n} \\ \\ \\ \-\hspace{2.3cm} = \displaystyle\frac{360^{\circ}}{21} \\ \\ \\ \-\hspace{2.3cm} = 17.14^{\circ} \ \ \ (\text{2 d.p.})[/tex].
which sum is
[tex]\text{Sum of exterior angles} \ = \ 17.14^{\circ} \ \times \ 21 \\ \\ \\ \-\hspace{3.59cm} = \ 360.0^{\circ}[/tex],
agrees with the theorem mentioned above.
