And yes `n` = 12 so expect to find some confetti on your head soon!

But Miss Loi prefers to do it this way:

As described, the diagram is highly inaccurate BUT for sure you'll see a 5-sided polygon (even though it's irregular). This will be the ONLY time Miss Loi uses the diagram.

Now by substituting `n` = 5 into the formula, you'll get:

45^{o} + 45^{o} + 3`x` = (5-2)180^{o}

where `x` is each of the unknown interior angle of the polygon.

Solving for this you'll get `x` = 150^{o}.

Next, if each interior angle of this `n`-sided polygon is 150^{o}, then the sum of all the interior angles will be 150^{o}*`n`. So we can derive the final equation:

150^{o}*`n` = (n-2)180^{o}

If you solve this you'll get `n` =12 too!

Well to each his/her own. But in this case, Miss Loi personally prefers the reliability of equations than to make potentially risky assumptions on inaccurate diagrams.

But well done and thanks for solving this pre-pubescent question!

]]>http://img509.imageshack.us/img509/6047/solutionks5.jpg ]]>

BUT even though the diagram can't accurately depict an `n`-sided polygon, it does a fine job of depicting another polygon with a *finite* number of sides.

Get the drift?

]]>Errr ... one reason for putting up this question is to show students that sometimes a diagram can be more bane than boon!

In this case you shouldn't be scrutinizing the finer points of the diagram - you will get more confused the longer you stare at it!

Focus on the given formula instead!

]]>