The sum of all measures of interior angles in a polygon with n sides is given by formula [tex] (n-2)180^{\circ} [/tex].
The sum of all measures of exterior angles in a polygon with n sides is always [tex]360^{\circ} [/tex].
Then
A) For a pentagon, n=5.
The sum of all measures of interior angles in a pentagon is [tex] (5-2)180^{\circ} =540^{\circ}[/tex].
B) For a 16-sided polygon, n=16.
The sum of all measures of interior angles in a 16-sided polygon is [tex] (16-2)180^{\circ} =2520^{\circ}[/tex].
B) For a dodecagon, n=12.
The sum of all measures of interior angles in a dodecagon is [tex] (12-2)180^{\circ} =1800^{\circ}[/tex].
If these polygons are regular or equiangular, then
A) Interiror angle has measure [tex] \dfrac{540^{\circ}}{5} =108^{\circ} [/tex] and exterior angle has measure [tex] \dfrac{360^{\circ}}{5} =72^{\circ} [/tex].
B) Interiror angle has measure [tex] \dfrac{2520^{\circ}}{16} =157.5^{\circ} [/tex] and exterior angle has measure [tex] \dfrac{360^{\circ}}{16} =22.5^{\circ} [/tex].
C) Interiror angle has measure [tex] \dfrac{1800^{\circ}}{12} =150^{\circ} [/tex] and exterior angle has measure [tex] \dfrac{360^{\circ}}{12} =30^{\circ} [/tex].
