Math, asked by kavehlalkaka, 1 month ago

One interior angle of an eight sided polygon is 1000 and the other angles are equal .Find the measurement of each equal angle

Answers

Answered by GangsterTeddy
12

Answer :-

140°

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)

So,

Total sum of angles in and 8 sided polygon = 180° * (8-2) = 1080°

Let the equal angles be x each

100° + 7x = 1080°

7x = 980°

x = 140°

Hope it helps ya cheerioo...

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