Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 4 | E Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
How do I find n?
Date Posted: 5 years ago
Views: 214
Let a be the angle of the polygon.
a= [(n-2) *180]/ n
(1): an= 180n -360
a+21 = [(n+7-2)*180]/(n+7)
an + 21n + 7a +147= 180n+ 900
(2): an + 7a = 159n + 753
(1) - (2): -7a = 21n - 1113
a= 159-3n
Sub a= 159-3n into (1),
(159 -3n)n = 180n - 360
159n - 3n^2 = 180n -360
3n^2 +21n -360 = 0
(n -8)(n+15) =0
Thus, n = 8.
a= [(n-2) *180]/ n
(1): an= 180n -360
a+21 = [(n+7-2)*180]/(n+7)
an + 21n + 7a +147= 180n+ 900
(2): an + 7a = 159n + 753
(1) - (2): -7a = 21n - 1113
a= 159-3n
Sub a= 159-3n into (1),
(159 -3n)n = 180n - 360
159n - 3n^2 = 180n -360
3n^2 +21n -360 = 0
(n -8)(n+15) =0
Thus, n = 8.
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Hope this helps, impt parts in pink !
Date Posted:
5 years ago
I presume using exterior angles would be easier.
With an increase of 7 sides, the exterior angle decreases by 21 degrees. Let exterior be called x.
nx = 360
(n + 7)(x - 21) = 360
Simultaneous approach.
With an increase of 7 sides, the exterior angle decreases by 21 degrees. Let exterior be called x.
nx = 360
(n + 7)(x - 21) = 360
Simultaneous approach.
360 Tutoring Program