the sum of interior angles of a regular polygon is twice the sum of its exterior angles.find the number of sides of polygon.

Asked by manmeetbatth79 | 25th Feb, 2015, 04:50: PM

Expert Answer:

L e t space n space b e space t h e space n u m b e r space o f space s i d e s space o f space t h e space p o l y g o n. H e n c e space t h e r e space a r e space n space i n t e r i o r space a n g l e s. W e space h a v e comma space s u m space o f space n space i n t e r i o r space a n g l e s space i s space open parentheses n minus 2 close parentheses cross times 180 degree W e space k n o w space t h a t space t h e space s u m space o f space e x t e r i o r space a n g l e s s space o f space a space p o l y g o n space i s space 360 degree. G i v e n space t h a t comma open parentheses n minus 2 close parentheses cross times 180 degree equals 2 cross times 360 degree rightwards double arrow open parentheses n minus 2 close parentheses equals fraction numerator 2 cross times 360 degree over denominator 180 degree end fraction rightwards double arrow n minus 2 equals 4 rightwards double arrow n equals 4 plus 2 equals 6 S o space t h e r e space a r e space 6 space s i d e s. T h e r e f o r e comma space i n space a space h e x a g o n comma space t h e space s u m space o f space i n t e r i o r space a n g l e s space i s space t w i c e space t h e space s u m space o f space i t s space e x t e r i o r space a n g l e s.

Answered by Vimala Ramamurthy | 26th Feb, 2015, 09:05: AM

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