The table below shows some information about regular polygons - Junior Cycle Mathematics - Question 14 - 2017
Question 14
The table below shows some information about regular polygons.
These are shapes where all of the angles are the same size.
| Number of angles in the polygon | Part ... show full transcript
Worked Solution & Example Answer:The table below shows some information about regular polygons - Junior Cycle Mathematics - Question 14 - 2017
Step 1
The sum of the angles in a polygon with 3, 4, 5, and 6 sides
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Answer
For the polygons given, we can determine the sum of the angles using the formula:
extSumofangles=(n−2)imes180exto
Where n is the number of sides. Therefore:
For n=3: (3−2)imes180exto=180exto
For n=4: (4−2)imes180exto=360exto
For n=5: (5−2)imes180exto=540exto
For n=6: (6−2)imes180exto=720exto
Step 2
Find a formula for the sum of the angles in a regular polygon with n angles
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Answer
The formula for the sum of the angles in a regular polygon with n angles can be expressed as:
extSumofangles=(n−2)imes180exto
Step 3
Complete the column in the table showing the size of each angle in each of these shapes
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Answer
The size of each angle in a regular polygon can be calculated using the formula:
extSizeofeachangle=n(n−2)imes180exto
Thus:
For n=3: rac{180^{ ext{o}}}{3} = 60^{ ext{o}}
For n=4: rac{360^{ ext{o}}}{4} = 90^{ ext{o}}
For n=5: rac{540^{ ext{o}}}{5} = 108^{ ext{o}}
For n=6: rac{720^{ ext{o}}}{6} = 120^{ ext{o}}
Step 4
Find a formula for the size of each angle in a regular polygon with n angles
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Answer
The formula for the size of each angle in a regular polygon can be expressed as:
extSizeofeachangle=n(n−2)imes180exto
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