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## #1 2008-04-15 15:23:06

stellina91
Member
Registered: 2008-04-15
Posts: 12

### Polygon

Find the value of a in the diagram, giving all reasons

My attempt:

180(5-2) = 540 (What would be the reason here?  E.g. Interior angle sum of an irregular pentagon)

2a + a + 104 + 125 + 107 = 540
3a + 336 = 540
3a = 204
a = 68

Thanks.

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## #2 2008-04-15 16:20:39

LuisRodg
Real Member
Registered: 2007-10-23
Posts: 322

### Re: Polygon

Your right. What do you need help with? Just checking if you were right?

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## #3 2008-04-15 16:23:12

Member
Registered: 2008-01-16
Posts: 147

### Re: Polygon

You will see in this way. When you divided it into 3 triangle, the sum  of interior is actually the sum of the interior of the 3 triangles , so 3*180=540 degree

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## #4 2008-04-15 16:25:43

LuisRodg
Real Member
Registered: 2007-10-23
Posts: 322

### Re: Polygon

Theres actually a formula to figuring out the sum of the angles of a polygon:

180(n-2) where n is the sides of the polygon.

Which I see he/she used by doing 180(5-2) = 540.

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## #5 2008-04-15 16:27:46

Member
Registered: 2008-01-16
Posts: 147

### Re: Polygon

LuisRodg wrote:

Theres actually a formula to figuring out the sum of the angles of a polygon:

180(n-2) where n is the sides of the polygon.

Which I see he/she used by doing 180(5-2) = 540.

yea, but he wanted to know why

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## #6 2017-05-19 15:59:55

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

### Re: Polygon

LuisRodg wrote:

Theres actually a formula to figuring out the sum of the angles of a polygon:

180(n-2) where n is the sides of the polygon.

Which I see he/she used by doing 180(5-2) = 540.

yea, but he wanted to know why

Well, I have tried to prove that, using sectors of a circle. Make a circle, then divide it to five equal sectors. After that, make a regular pentagon inside the circle. Each sector will have 72° as their radius angle. From this, you can know that each angle of the pentagon is 108°. Multiplying it by 5 will give 540°. You can do for other polygons to get similar proof.

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