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Question Number 55561 by otchereabdullai@gmail.com last updated on 26/Feb/19

Commented by otchereabdullai@gmail.com last updated on 26/Feb/19

$p r o f W p l e a s e a m l e a r n i n g t h i s q u e s t i o n$ $s o l v e d f o r m e o n t h e 21 s t b u t i d o n t$ $u n d e r s t a n d t h i s p a r t : i f n = 16 : α_{n} = - 5 < 0$ $a n d i f n = 18 : α_{n} = 355 > 180$ $a n d h o w y o u g o t t h e n = 17 .$ $p l e a s e h e l p m e p r o f W$
Commented by mr W last updated on 27/Feb/19

$w e h a v e g o t$ $α_{n} = (n - 2) \times 180 ° - 2525 °$ $w e w a n t t o f i n d h o w l a r g e n i s s u c h$ $t h a t 0 < α_{n} < 180 ° .$ $i f w e p u t (n - 2) \times 180 ° - 2525 ° = 0, w e$ $g e t n \approx 16.03 . n o w w e t r y w i t h n = 16,$ $w e g e t α_{n} = (16 - 2) \times 180 - 2525 = - 5 °,$ $w h i c h i s n o t o k, i . e . n \neq 16 .$ $t h e n w e t r y w i t h n = 17, w e g e t$ $α_{n} = (17 - 2) \times 180 - 2525 = 175 °, t h i s i s$ $o k . b u t i s n = 17 t h e o n l y o n e s o l u t i o n ?$ ${l e t}^{'} s t r y w i t h n = 18, a n d w e g e t$ $α_{n} = (18 - 2) \times 180 - 2525 = 355 °, t h i s i s$ $n o t o k . t h a t m e a n s n = 17 i s t h e o n l y$ $o n e s o l u t i o n .$
Commented by otchereabdullai@gmail.com last updated on 26/Feb/19

$w o w! w o w! I n f a c t y o u a r e a n i d e a l$ $p r o f!$
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