Question

pls solve this problem ​

Answer 1

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)

Now the main answer,

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

Hope it helps!!

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