polygon inside circle

匿名

2011-07-27 10:08 am

1個圓形，入面有1個不規則ge 8邊形
由順時針數8邊形內角，第1隻角係a，第2隻唔知，第3隻係b,第4隻唔知......
a+b+c+d=?
ans is 540
but i don't know why?
explain plz

And search: present value of f.4 math
都係我ge，幫手答

回答 (1)

用戶10012

2011-07-27 3:49 pm

✔ 最佳答案

Let O be center of the circle.
Let the angles at O that are opposite to angles a, b, c and d be x, y, z and m respectively. That is x + y + z + m = 360 degrees ( angles at a point).
By property of circle : angle at circumference is half angle at center, we get:
a = (y + z + m)/2.............(1)
b = (x + z + m)/2.............(2)
c = (x + y + m)/2.............(3)
d = (x + y + z)/2..............(4)
Adding them together, we get
a + b + c + d = (y + z + m + x + z + m + x + y + m + x + y + z)/2
= 3(x + y + z + m)/2 = 3 x 360/2 = 3 x 180 = 540 degrees.

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