Polygons and Symmetry 1

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satis · Answer

The sum of the interior angles of a regular polygon is : (n - 2) × 180°,where  n  is the number of sides of the polygon. The sides and the angles of a regular polygon have equal measures.
  
The Sum of the measures of the exterior angles of a polygon is always 360°, and measure of each exterior angle of a regular polygon = 360°/n, where  n  is the number of sides of the polygon
  
Hexagon has six sides.
  Pentagon has 5 sides as well as 5 angles .  
  The sum of the measures of the exterior angles of a pentagon
  The given polygon is a Heptagon with 7 no. of sides
  
Sum of the measures of the interior angles of a hexagon :
  
=  (n - 2) × 180° = (6 - 2) × 180° = 720°
    
 
  
The sum of the measures of the interior angles of a pentagon is   
= (n - 2) × 180° = (5 - 2) × 180° = 540°
    
Thus, the measure of each interior angle of a regular pentagon is 
  
= 540°/5 = 108°
    
 
  
= Supplimentary angle  of each interior angle x no. of sides
  
= (180° - 108o) x 5 = 360°
    
 
  
The sum of the measures of the interior angles of a heptagon is   
= (n - 2) × 180° = (7 - 2) × 180° = 900°

summoremath2 · Answer

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ultrarunner33 · Answer

1. You are using the formula (n – 2)180 degrees  n is the number of sides of your ____gon in this case we have a hexagon or a 6 sided figure therefore (6-2)180 degrees = 720 degrees or the sum of the interior angles of a hexagon
2. Using the same formula and reasoning as in number one we are now substituting 5 for n because there are 5 sides on a pentagon (5-2)180 degrees = 540 degrees Now we know each angle is equal so we can simply divide this by 5 and get 108 degrees for the measure of each angle.
3. Since a pentagon is considered a regular polygon we can take 360/n which is 360/5 or 72 degrees for the exterior angle
4. We have a 7- gon here and we are given all but one angle to get the sum of all known angles we add them and get 789 degrees  using (n-2)180    (7-2)180 = 900 degrees this number minus 789 = 111 degrees which is your x
5. just as in 3 we simply take 360/6 = 60 degrees

kpraveer · Answer

Sum of interior angles = (Number of sides - 2) * 180, exterior angle is always 360.1) (6 - 2) * 180 = 720 degrees.2) (5 -2) * 180 = 540 degrees for 5 equal angles, hence 108 degrees each angle.3) 360 degrees.4) sum of all angles = (7 - 2) * 180 = 900 degrees. Sum of given angles = 125 + 126 + 158 + 120 + 121 + 139 = 789 degrees   x = 111 degrees5) 360 / 6 = 60 degrees

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Polygons and Symmetry 1

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