http://img205.imageshack.us/my.php?image=watim3.jpg

Take a look at this picture here. All the numbers listed are angles in degrees. Diagram is not drawn to scale.

There are two unknowns, x and the value of the blank side. (The x + 150 is on the outside of the pentagon, it's for the exterior angle).

How would you go about finding the value of x and the blank side on the top, stopping short of guessing?

I found that if you do an equation like this, by subbing 150 in for the blank side.

540=130 + 130 + 10 + x + x + 150
120=2x
x=60

Therefore: 60 + 10 + 60 + 130 + 130 + 150 = 540

It works, but I don't understand, does this method work for other questions of different values like this?

Can someone help me explain the relationship between the exterior angle (x + 150) and the value of the interior angle, and why you can work out the value of the blank interior angle by substituting 150?

Their all angles right? Cant you do some simple trig to get the height, then work out the angle?

does x = 80?

The corners are presumably square, and if the it is an angle, then it would be 90deg. But then it would mess the other calculations, as it would be 80deg for the other corner, and 230 for the top. Hmm......Maybe draw it to scale, and use a protractor to get the angles and then figure out a formula?

Dunno, this probably just confused you more then it did me....

Is it possible the bottom 2 angles are different? Like x = 90, and x + 10 = 100?

So x + 150 = 240?

It's gotta equal 360 for the top, so if you know the inside angle, then you use the remaining(x + 150) to figure out x for the bottom ones.

This has just been a random babble, so if it doesnt help, just flame or whatever

are you trying to find x and the top interior angle?

if so, listen up.

let the interior angle be y

the sum of the interior angles in a polygon is 180*(n-2) where n is the number of vertices in that shape. in this case, it is 5
=180*3
=540

so the sum of the angles = 540
y+130+x+x+10+130 = 540

2x + y = 270
y=270-2x

we also know that the interior + exterior angle = 360 (angles at a point add up to 360)
x+150 +y = 360
x +y=210

now sub the first bolded equation into the second.
x + 270 -2x =210
-x = -60
x=60
substitute x=60 into any of the bolded equations, lets use the second one
60+y=210
y=150
for fun, lets sub x=60 back into the first bolded equation
y= 270 - 2*60
=270 - 120
=150


therefore, x = 60 and the interior angle =150

youre welcome

if you decide to do maths in university, you will learn the beauty of gaussian elimination, which you can use to solve many variables!

I think mantikore tried to help you understand why 150 works, but I'm not sure he did a good job of explaining it, so if you don't still, actually bother to read my post.

So:

540= x + 10 + x + 130 + 130 + (360 - x - 150)

x = 60

What you did was just insert 150 in the place of the parentheses in my equation, right? That represents the measure of the interior angle based on the information we were giver. So, right. Here's why it works:

360 - x - 150 = 150

360 = 300 + x

Now, define the x.

360 = 300 + 60 is true. This is just a coincidence, that simply plugging in 150 as the number works. Don't expect that to keep coming up. Sorry if I'm being redundant.