Okay, I've posted after a long time, I know... But I'm here with another doubt.

The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

Thanks!

Printable View

- January 6th 2007, 06:14 AMRuler of HellPolygons Help!
Okay, I've posted after a long time, I know... But I'm here with another doubt.

The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

Thanks! - January 6th 2007, 06:34 AMCaptainBlack
Let the number of sides of the polygons be and , then the first condition tell you that:

,

and as the interior angle of a ploygon with sides is , the second condition tells us that:

which may be simplified as we know to:

Now we can proceed to solve and , or we can just guess, when we find , .

RonL - January 6th 2007, 06:50 AMRuler of Hell
Wait, I'm still a li'l confused. How did you solve equation 1 and 2? Sorry....

- January 6th 2007, 06:53 AMCaptainBlack
- January 6th 2007, 07:06 AMRuler of Hell
Got it! Yay, thanks a tonne Captain Black... (Though I used 2 different methods, yours and another one) Nonetheless, thanks!