How many sides does this mysterious polygon have ?

Level pending

The exterior angle of a regular 18-sided polygon is 88° less than the exterior angle of a regular n-sided polygon. Find the value of n.

1 solution

Yoel Susanto
Feb 24, 2014

$180\quad -\quad \frac { ({ n }_{ 1 }-2)\times 180 }{ { n }_{ 1 } } \quad =\quad \frac { ({ n }_{ 2 }-2)\times 180 }{ { n }_{ 2 } } -88$

$180\quad -\quad \frac { (18-2)\times 180 }{ 18 } \quad =\quad \frac { ({ n }_{ 2 }-2)\times 180 }{ { n }_{ 2 } } -88$

$180\quad -\quad \left( 16\quad \times \quad \frac { 180 }{ 18 } \right) \quad =\quad \frac { ({ n }_{ 2 }-2)\times 180 }{ { n }_{ 2 } } -88$

$180\quad -\quad 160\quad =\quad \frac { ({ n }_{ 2 }-2)\times 180 }{ { n }_{ 2 } } -88$

$20\quad =\quad \frac { ({ n }_{ 2 }-2)\times 180-88{ n }_{ 2 }\quad }{ { n }_{ 2 } }$

$20{ n }_{ 2 }\quad =\quad { 180n }_{ 2 }-360-88{ n }_{ 2 }$

$360\quad =\quad { 92n }_{ 2 }-20{ n }_{ 2 }$

${ n }_{ 2 }\quad =\quad 5$