F. 2 Maths 不明白，想要詳細橫式作參考

2009-09-13 11:43 pm

1) If an exterior angle of a regular polygon is 24° less then 1/6 of its interior angle, find the number of sides of the regular polygon.

2) If the exterior angles of a convex hexagon are x, 3x, 5x, 7x, 9x and 11x respectively, find the size of the largest exterior angle.

3) If an interior angle of a regular polygon is 5 times its exterior angle, fine the number of sides of the regular polygon.

4) If twice of an interior angle of a regular polygon is 144° more than its exterior angle, find the number of sides of the regular golygon.

回答 (1)

仔

2009-09-17 6:47 pm

✔ 最佳答案

1) Ext(X) + Int = 180degree (angles on a straight line)
X + (X + 24)6 = 180
7X + 144 = 180
X = 36 / 7

The regular polygon is a:
360 degree divided by 36 / 7 (sum of ext. angles of a polygon is 360 degrees)
= 360 x 7/36
= 70

2)
x + 3x + 5x + 7x + 9x + 11x = 360
x = 10

size of the largest exterior angle:

=11x , therefore
=110 degree

3) and 4)： similar method used in 1) and 2)，自己試下啦!

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