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!
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!
Let the number of sides of the polygons be $\displaystyle n$ and $\displaystyle m$, then the first condition tell you that:
$\displaystyle \frac{n}{m}=\frac{4}{5}\ \ \ \dots(1) $,
and as the interior angle of a ploygon with $\displaystyle n$ sides is $\displaystyle 180(n-2)/n$, the second condition tells us that:
$\displaystyle
\frac{n-2}{n}\,\frac{m}{m-2}=\frac{15}{16}
$
which may be simplified as we know $\displaystyle n/m=4/5$ to:
$\displaystyle
\frac{n-2}{m-2}=\frac{3}{4}\ \ \ \dots(2)
$
Now we can proceed to solve $\displaystyle (1)$ and $\displaystyle (2)$, or we can just guess, when we find $\displaystyle n=8$, $\displaystyle m=10$.
RonL