Geometry Question

[Crickleymal]

Ok not a self sufficiency question, but there must be some mathematicians here. Normally I'm good at maths but for some reason this one has me stumped.

GCSE practice paper.
Sum of angles in a polygon of n sides = 180n-360.

A polygon has 2 corners with internal angle 90 degrees. The remaining corners all have angles (internal presumably) of 144 degrees. How many sides does the polygon have?

[GeorgeSalt]

Sum of angles = 180n - 360 = 180(n-2)

2(90) + (n-2)(144) = 180n - 360
180 + 144n -188 = 180n - 360
352 +144n = 180n
352 = 36n
9.778 = n ???

Something not riight there.. but I cant see where I'm going wrong.. how have you tackled it?

Just in case, 180 - 144 = 36

2(90) + (n-2)(36) = 180n - 360
180 + 36n - 36 = 180n - 360
504 = 144n
3.5 = n

From dragging around the irregular polygon points on this page I know the answer should be 7. I can't get it to work though.. too late tonight I suspect. I'll look again tomorrow.

[GeorgeSalt]

Ok.. I can get it to work backwards, so it's a simple error somewhere..

180n - 360 = 720 <-- for n=7
720 - 90 - 90 = 720
720 / 5 = 144

I see the error I've made..

2(90) + (n-2)(144) = 180n - 360
180 + 144n - 288 = 180n - 360
180 - 288 + 360 + 144n = 180n
252 +144n = 180n
252 = 36n
7 = n

There you go..

[Crickleymal]

Thanks. I had a brainwave last night about 11:30 and that is the exact reasoning that I came up with.

[marshlander]

Is this you?

[GeorgeSalt]

It's only GCSE algebra (algebra hidden within a geometry question).. .. and that's a very useful type of question to be able to solve for an -isher (maybe not the polygon example).


Your homework for tonight, all working must be shown ;)

If 1lb of raspberries and 1lb of sugar makes three 10oz jars of jam, how many raspberries and how much sugar do I need to fill a dozen half-pound jars?

If 5lb plums and 3lb sugar makes a gallon of plum wine, how much wine can I make with 12lb and how much sugar will I need?

[Crickleymal]

Relatively easy too. 2lb of ingredients (32oz) molishes 30oz jam. so 1 oz of ingredients makes 30/32oz or 15/16oz. You want to fill 12 8oz jars or 96 oz. so you need 96/(15/16) which is 102.4 oz of ingredients or 3.2lb rasberries and 3.2lb sugar.

[marshlander]

Depends how many raspberries I eat before they get to the pot!

[GeorgeSalt]

Depends how many raspberries I eat before they get to the pot!

I can add a variable for that if it would make it any easier.. .. .. ;)

[Crickleymal]

I remember on one training course (on a radiotherapy machine) one of the test questions at the end was "How many screws have to be taken out to remove the finger guard plates?" The answer could be 44 or "too many" depending on how lenient the marker was.