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