maths1`問...(f2).............................................

2008-02-24 7:19 am

1. )If each interior angle of a regular polygon is 140°,tthen how many sides does it have?
2. )Each interior angle of a regular polygon is 108° more than each exterior angle.How many sides are there in this polygon?
3.) If the interior angles of a convex pentagon are x-25°,x-10°,x,2x and 2x+15°,find
a. the value of x.
b. the measure of the smallest interior angle.
c. the measure of the smallest exterior angle.

回答 (1)

志仁

2008-02-24 7:53 am

✔ 最佳答案

1) degree of the total sum of internal angles=180(n-2)
each internal angle = 180(n-2)/n = 140
180n-360=140n, n=9
2) internal + external = 180
internal - external = 108
2 internal = 288, each internal = 144 = 180(n-2)/n
360=36n, n=10
3a) Sum of the internal angle =(5-2)180=540=(x-25)+(x-10)+x+2x+(2x+15)
7x-20=540, x=80
b) The smallest internal angle=x-25=55
c) The smallest external angle, we need to find the max. internal angle
max. internal angle=2x+15=175, internal + external = 180, then the smallest external angle=5

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