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in Polygons by (30.3k points)
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What is the sum of all interior angles of a regular 

(i) pentagon 

(ii) hexagon 

(iii) nonagon 

(iv) polygon of 12 sides

1 Answer

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Best answer

(i) In Regular Pentagon, all sides are of same size and measure of all interior angles are same. 

The sum of interior angles of regular pentagon is 

= (n – 2) × 180° [n is number of sides of polygon)] 

= (5 – 2) x 180° 

= 540° .

(ii) In Regular Hexagon, all sides are of same size and measure of all interior angles are same. 

The sum of interior angles of regular hexagon is 

= (n – 2) × 180° [n is number of sides of polygon)] 

= (6 – 2) x 180° 

= 720°

(iii) In Regular Nonagon, all sides are of same size and measure of all interior angles are same. 

The sum of interior angles of regular nonagon is 

= (n – 2) × 180° [n is number of sides of polygon)] 

= (9 – 2) x 180° 

= 1260°

(iv) In Regular Polygon of 12 sides, all sides are of same size and measure of all interior angles are same. 

The sum of interior angles of regular polygon of 12 sides is 

= (n – 2) × 180° [n is number of sides of polygon)] 

= (12 – 2) x 180° 

= 1800°

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