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### 多邊形的種類及內角和

• 定義：多邊形(polygon)是由三條或以上的直線所圍成的平面圖形。

A1. 按形狀凹凸分類的多邊形

A2. 按各邊及各角相等情況分類的多邊形

△內角和

A+B+C=180°

A

B

C

A+B+C=180°

A+C+D=180°

=360°

A

B

D

C

=540°

A

B

E

C

D

• 根據以上例子，從而求各多邊形的內角和。

4

4X 180° = 720°

5

5X 180° = 900°

6

6X 180° = 1080°

7

7X 180° = 1260°

8

8X 180° = 1440°

n-2

( n-2 )X 180°

n邊的內角和是 ( n-2 )X 180°。

[ 簡記：多邊形內角和 ]

• 練習一：求十八邊形的內角和
• 2520°
• 2700°
• 2800°
• 2880°
• 3060°

= ( n-2 )X 180°

= 16X 180°

= 2880°

• 2520°
• 2700°
• 2800°
• 2880°
• 3060°

B

80°

• 98°
• 100°
• 1100°
• 120°
• 130°

A

50°

100°

χ

C

D

X+230 °= 2X 180°

X+230 °= 360°

x= 360° - 230°

x= 130°

B

80°

• 98°
• 100°
• 1100°
• 120°
• 130°

A

50°

100°

χ

C

D

A

B

• 75°
• 85°
• 90°
• 100°
• 105°

y

150°

y

E

C

2y

D

4y+240 ° = 3X 180°

4y+240 ° = 540°

4y = 540° - 240°

4y = 300°

y = 75°

A

B

• 75°
• 85°
• 90°
• 100°
• 105°

y

150°

y

E

C

2y

D

• 100°
• 120°
• 140°
• 150°
• 160°

y

6y = 4X 180°

6y = 720°

y = 120°

• 100°
• 120°
• 140°
• 150°
• 160°

y