Question 1116540: Sarah has some large, polygon-shaped cardboard cutouts that she needs to sort, because she wants to hang them in her geometry classroom. The first division she needs to make is to divide the regular polygons from the irregular ones. In order to save time measuring all angles and sides of each polygon, and owing to the size and number of sides/angles in each shape, Sarah decides to measure just one angle in each polygon. Consider the following angle measures for polygons A through T, and answer the following questions.
A B C D E F G H I J
10 15 20 30 40 45 50 60 72 75
K L M N O P Q R S T
80 90 100 108 120 144 150 210 240 360
a. If each angle measure represented an exterior measure of its polygon, which of the polygons could be regular? Explain your answers.
b. If each angle measure represented an exterior measure of a regular polygon, name each polygon by using its number of sides. (For any figure with more than 12 sides, just use the number: e.g. 45-gon.)
c. If each angle measure represented an exterior measure of its polygon, which of the polygons could be regular? Explain your answers.
d. If each angle measure represented an exterior measure of its polygon, which of the polygons do we know are convex? Explain your answers.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider the following angle measures for polygons A through T, and answer the following questions.
A B C D E F G H I J
10 15 20 30 40 45 50 60 72 75
K L M N O P Q R S T
80 90 100 108 120 144 150 210 240 360
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Note:: The sum of the exterior angles is always 360 degrees.
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a. If each angle measure represented an exterior measure of its polygon, which of the polygons could be regular? Explain your answers.
b. If each angle measure represented an exterior measure of a regular polygon, name each polygon by using its number of sides. (For any figure with more than 12 sides, just use the number: e.g. 45-gon.)
A:: 360/10 = 36; regular: 36-gon
B:: 360/15 = 24; regular; 24-gon
C:: 360/20 = 18; regular; 18-gon
D:: 360/30 = 12; regular; duodecagon
...
G:: 360/50 = 7.2; not regular
...
I:: 360/72 = 5; regular; pentagon
etc.
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d. If each angle measure represented an exterior measure of its polygon, which of the polygons do we know are convex? Explain your answers.
M,N,O,P etc. have exterior greater than 90 degrees so they are convex.
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Cheers,
Stan H.
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