Each interior angle if a regular polygon is 18 more than eight times an exterior angle. The number of sides of the polygon is

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Solution

Dear student,

$L e t' x' b e t h e i n t e r i o r a n g l e o f a t h e r e g u l a r p o l y g o n t h e n, e x t e r i o r a n g l e i s (180 - x) A c c o r d i n g t o q u e s t i o n, x = 8 (180 - x) + 18 \Rightarrow x = 1440 - 8 x + 18 \Rightarrow x + 8 x = 1440 + 18 \Rightarrow 9 x = 1458 \Rightarrow x = \frac{1458}{9} \Rightarrow x = 162 T h u s t h e m e a s u r e o f e a c h a n g l e i s 162 ° t h e n e x t e r i o r a n g l e s i s 180 ° - 162 ° = 18 ° E x t e r i o r a n g l e = \frac{360 °}{n} \Rightarrow 18 ° = \frac{360 °}{n} \Rightarrow n = \frac{360 °}{18 °} \Rightarrow n = 20 s o, t h e n u m b e r o f s i d e s = 20$
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