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ICSE - VIII - Mathematics - Special Types of Quadrilaterals

an exterior angle of a regulsr polygon is one-fourth of its interior angle.find the number of sides in the polygon.

Asked by manmeetbatth79 25th February 2015, 4:54 PM
Answered by Expert

Answer:

L e t space x space b e space t h e space e x t e r i o r space a n g l e space o f space a space r e g u l a r space p o l y g o n space a n d space y space b e space t h e space c o r r e s p o n d i n g space i n e t r i o r space a n g l e space o f space a space p o l y g o n. G i v e n space t h a t space e x t e r i o r space a n g l e space i s space o n e space f o u r t h space o f space i t s space i n t e r i o r space a n g l e. rightwards double arrow x equals y over 4... left parenthesis 1 right parenthesis S i n c e space x space a n d space y space a r e space e x t e r i o r space a n d space c o r r e s p o n d i n g space i n t e r i o r space a n g l e comma space w e space h a v e comma space x plus y equals 180 degree rightwards double arrow y over 4 plus y equals 180 degree space space space space space open square brackets because space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis close square brackets rightwards double arrow y plus 4 y equals 180 degree rightwards double arrow 5 y equals 180 degree rightwards double arrow y equals fraction numerator 180 degree over denominator 5 end fraction rightwards double arrow y equals 36 degree rightwards double arrow x equals 180 degree minus 36 degree equals 144 degree I f space e a c h space e x t e r i o r space a n g l e space o f space a space r e g u l a r space p o l y g o n space i s space A degree comma space t h e n space t h e space n u m b r space o f space s i d e s space i n space t h e space p o l y g o n equals fraction numerator 360 degree over denominator A end fraction S i n c e space e x t e r i o r space a n g l e space i s space 36 degree comma space t h e space n u m b e r space o f space s i d e s space i n space t h e space p o l y g o n equals fraction numerator 360 degree over denominator 36 degree end fraction equals 10
Answered by Expert 26th February 2015, 9:30 AM

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