Question

PLEASE HELP ME WITH GEOMETRY WORK

Answer 1

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

`\text{Exterior angle} \ = \ \displaystyle(360)/(n)`.

Hence, for a convex 21 sided-polygon (henicosagon), each exterior angle will be

`\text{Exterior angle} \ = \ \displaystyle(360^(\circ))/(n) \\ \\ \\ \-\hspace{2.3cm} = \displaystyle(360^(\circ))/(21) \\ \\ \\ \-\hspace{2.3cm} = 17.14^(\circ) \ \ \ (\text{2 d.p.})`.

which sum is

`\text{Sum of exterior angles} \ = \ 17.14^(\circ) \ * \ 21 \\ \\ \\ \-\hspace{3.59cm} = \ 360.0^(\circ)`,

agrees with the theorem mentioned above.