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**Math Student****Guest**

1)

A heptagon has 6 equal angles x and one angle 2x. Find the value of x.

2)

PQ is one side of a regualar polygon with centre O.

If y=4 (1/2)x find the number of sides in the polygon.

3)

Half of the exterior angles of a polygon are 8° and the other exterior angles are each 12° . How many sides has the polygon?

**Math Student****Guest**

Don't nother wiht munber 2! I've worked that one out.

Oh yes, for number 1 could you draw the shape out for me? I found out that the angle should be 112.5° but I'm not sure if that is right.

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

1) A heptagon has (7-2)*180 = 900 degrees totalling its internal angles.

All of the internal angles in this heptagon total 8x. Therefore, x = 900/8 = 125°

2) I won't bother explaining because you've done it and the explanation is lengthy, but I got it to be a hexagon. Am I right?

3) The external angles of a polygon always add to 360°. The average external angle is (8+12)/2 = 10°, so there are 360/10 = 36 sides.

Why did the vector cross the road?

It wanted to be normal.

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**Math Student****Guest**

There was a mistake with your number 1. 900/8 is 112.5 not 125. I got 112.5 but I can't draw the shape.

For number 2 I got 20?

The bottom two angles are:

4 1/2x +4 1/2x

9x/2 + 9x/2 = 18x/2 = 9x

9x+x = 10x

180° /10=18°

therefore

x=18°

360/18=20

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

1) Yes, you're right. Sorry.

2) I took 4 (1/2) to mean a strange way of saying 2, so you're right there as well. Sorry again.

Why did the vector cross the road?

It wanted to be normal.

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**Math Student****Guest**

Thanks for that.

Ermm... do you know how to draw the irregular septagon? I'm still having trouble with it.

Sorry about number 2. It's sometimes hard to show fractions

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,663

A septagon has 7 sides. If it is irregular, then it could have any variation of side lengths and angles.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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