B. Find the number of sides of the regular polygon when the sum of the measures of the vertex angles
are given. (Show your solutions)
Example: 720°
Solution: S = (n - 2 ) 180°
using the same formula
720° = (n-2) 180° substitute the given sum measures of the vertex angle
720 = 180°n - 360° multiply (n - 2 ) to 180°
720° + 360° = 180n transposition
1080° = 180n
divide both side of the equation by the coefficient 180
180 180
6
answer; 6 sides or hexagon
=n
3. 4320°
1. 1620°
2. 1980°
are given. (Show your solutions)
Example: 720°
Solution: S = (n - 2 ) 180°
using the same formula
720° = (n-2) 180° substitute the given sum measures of the vertex angle
720 = 180°n - 360° multiply (n - 2 ) to 180°
720° + 360° = 180n transposition
1080° = 180n
divide both side of the equation by the coefficient 180
180 180
6
answer; 6 sides or hexagon
=n
3. 4320°
1. 1620°
2. 1980°
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Answers & Comments
Answer:
1. 11 sides
2. 13 sides
3. 26 sides
Solutions:
1. 1620°=(n-2)180°
1620°=180°n-360°
1620°+360°=180°n
1980°=180°n
11=n
2. 1980°=(n-2)180°
1980°=180°n-360°
1980°+360°=180°n
2340°=180°n
13=n
3. 4320°=(n-2)180°
4320°=180°n-360°
4320°+360°=180°n
4680°=180°n
26=n