n is the number of sides in a polygon and 52 degree is the smallest angle and the other angles increases subsiquently by 8 degree .find n
Answers
Answer:
3 and 30
Step-by-step explanation:
(n-2) * 180° = total sum of all angles
Derivation : just take a n-sided polygon , from one vertex join all vertices except the adjacent ones(as they are already joined)
now you will see that you are getting (n-2) triangles everytime and so sum of all angles = (n-2)*180
Eg. in a quad we can draw 2 traingles like explained above,so sum of angles = (4-2) * 180 = 360
in a pentagon choose a vertex and then join other vertices , you will get 3 triangles so sum is 3*180 =540
(remember this formula if you don't know)
smallest angle is 52
a=52 , d =8
using sum of ap formula
sum of all angles = (n/2) (2*52+(n-1)*8) =(n/2)(8n+96) = 4n(n+12)
put it in the first equation
(n-2) * 180 = 4n(n+12)
45n - 90 = n^2 + 12n
n^2 - 33n + 90 = 0
solve to get n = 3,30
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Answer:
it may be a three sided polygon (or) thirty-sided polygon.
step by step explanation:
the sum of all interior angles of polygon is 180(n-2).
therefore ,
the angles are in A.P,
the common difference is(D)=8
=>52,52+8,52+16,52+24,.......
=>52,60,68,76........
here,(a)=52
(d)=8
=>Sn=n/2(2a+(n-1)d)
=>180(n-2) =n/2(2*52+8n-8)
=>180n-360=n(104+8n-8)/2
=>4n^2-132n+360=0
divideby(4),
=>n^2-33n+90=0
=>(n-30)(n-3)
therefore,
n=30 (or) n=3
HENCE IT IS A THREE SIDED POLYGON OR THIRTY SIDED POLYGON.
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