關系角度的中二數學題目一問

Let y be the number of sides.
Let x degree be the size of one exterior angle, then
(x+140) be the size of interior angle.

(x+140) = 140 + x(given )

(x+140) + x= 180 (adj. angles on st. line)
(x+140) = 180 - x

so,
180 - x= 140 + x
x = 20 degrees


y*x = 360 (sum of exterior angle of polygon)
y*20 = 360
y = 18


so, the number of sides the polygon has is 18.

首先，設每隻內角為x+140和每隻外角為x
x+(x+140)=180
x=20
然後外角的總和是360
所以只要將總和除每一隻外角=邊的總數
360/20=18
答案是正18邊形

Let x be the exterior angle of the polygon.
Therefore, interior angle = x + 140 (according to the question).
Since (x) + (x + 140) = 180 (adjacent angles on a straight line)
Therefore x=20.
Since sum of exterior angles of a polygon =360.
Therefore, number of sides of the polygon= 360/20=18.
That is the required polygon is an 18-sided polygon.