Question

One angle of an eight-sided polygon is 100° and the other angles are equal. Find the measure of each equal angle.

Answer 1

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°

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