The exterior angle of each polygon and the adjacent interior angle are
supplementary.
(a) 72° (b) [tex]\displaystyle 51 \frac{3}{7} ^{\circ}[/tex] (c) 36° (d) 20° (e) 18°
Reasons:
The formula for the exterior angle of a regular polygon is, [tex]\displaystyle \theta = \mathbf{ \frac{360 ^{\circ}}{n}}[/tex]
Where;
θ = The exterior angle of the polygon
n = The number of sides of the regular polygon
(a) The number of sides in a pentagon, n = 5 sides
Therefore, for a regular pentagon, we have;
[tex]Exterior \ angle , \displaystyle \theta = \frac{360 ^{\circ}}{5} = \mathbf{{72^{\circ}}}[/tex]
The measure of the exterior angle of a pentagon, is 72°
(b) An heptagon has n = 7 sides
The measure of the exterior angle, θ, of a regular heptagon is therefore;
[tex]Exterior \ angle \ of \ a \ heptagon , \,\displaystyle \theta = \frac{360 ^{\circ}}{7} = \underline{51 \frac{3}{7} ^{\circ}}[/tex]
(c) A decagon has n = 10 sides, which gives;
[tex]The \ exterior \ angle \ of \ a \regular \ decagon, \,\displaystyle \theta = \frac{360 ^{\circ}}{10} = \underline{36^{\circ}}[/tex]
(d) The exterior angle of an 18-gon with n = 18 sides is given as follows;
[tex]The \ exterior \ angle \ of \ a \ regular \ 18-gon, \,\displaystyle \theta = \frac{360 ^{\circ}}{18} = \underline{20^{\circ}}[/tex]
(e) A regular 20-gon has n = 20 sides
The exterior angle of a regular 20-gon is [tex]\displaystyle \frac{360 ^{\circ}}{20} = \underline{ 18^{\circ}}[/tex]
Learn more about the angles of a polygon here:
https://brainly.com/question/12871621
