# Two sets of geometric problems invlolving finding the measure of angles

• Jul 10th 2007, 12:19 PM
frostbite
Two sets of geometric problems invlolving finding the measure of angles
Sorry that the second problem is slanted--my scanner's acting weird. Here are the problems:

Attachment 3559

Attachment 3558

If you try to solve these, PLEASE check your work to see that you are correct. I really want to get both of these problems 100% correct. Also, please show all your work, even if it is a simple addition problem like 100+2.

Thank you!
• Jul 10th 2007, 01:08 PM
red_dog
The sum of angles of a n-polygon is $\displaystyle (n-2)180^{\circ}$.
The sum of angles of a pentagon is $\displaystyle 540^{\circ}$. If the pentagon is regular, then each angle is $\displaystyle 108^{\circ}$.
The sum of angles of a hexagon is $\displaystyle 720^{\circ}$. If the hexagon is regular, then each angle is $\displaystyle 120^{\circ}$.
Then $\displaystyle \widehat{BAE}=108^{\circ},\widehat{EAL}=120^{\circ }\Rightarrow \widehat{BAL}=\widehat{KLA}=360^{\circ}-120^{\circ}-108^{\circ}=132^{\circ}$.
$\displaystyle \widehat{ABK}=\frac{360^{\circ}-2\cdot 132^{\circ}}{2}=48^{\circ}$
• Jul 10th 2007, 01:14 PM
CaptainBlack
Quote:

Originally Posted by frostbite
If you try to solve these, PLEASE check your work to see that you are correct. I really want to get both of these problems 100% correct. Also, please show all your work, even if it is a simple addition problem like 100+2.

And will we get the credit for doing so? Don't you think that at the
very least you should be prepared to check the results and fill in
minor detail?

RonL
• Jul 10th 2007, 01:40 PM
frostbite
CaptainBlack, I'm sorry if my post came off as offensive. It wasn't meant to be read like that, but now in hindsight, I can see how it can be taken in the wrong way.
Most of the time when I'm doing a math problem (especially easier ones), I have a tendency to rush, often making silly mistakes. If the problem involves more than one step, this often leads me to a wrong conclusion, one that I probably could've gotten right if I slowed down.
Since most people on this forum are very accomplished in the field of mathematics I assumed that a problem that is difficult to me, a 15 year old, would be easy for them. This might have led them to a wrong conclusion, one which could in turn provide a wrong answer. If I too made the same mistake while looking over the problem, I would have gotten the question wrong.
Also regarding the note on showing work: people often think in differently. When looking over the equation, it's hard to follow, causing me to not understand their thought process. My 100+2 example was just an extreme example used to get my point across.
Please understand that I am not usually this haste (or rude) --it's just that these problems are very important to me; I've spent 30 minutes trying to solve each of them, and so far I came to no avail. This is for an extra credit assignment that I need, and since nobody in my family is strong in geometry, I was basically on my own.