Question

How many diagonals does a regular polygon has if it's interior angle is 150 °?

Answer 1

The interior angles are 150°
so the exterior angles are 180° - 150° = 30°
SUM OF EXTERIOR ANGLES = 360°
so if we divide 360° by 30° we find there are 12 exterior angles.
Therefore, there are 12 sides 
THUS DIAGONALS = N(N-3)/2 = 12(12-3)/2 = 12(9)/2 = 108/2 = 54 

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Answer 2

The interior angles are 150°

so the exterior angles are 180° - 150° = 30°

SUM OF EXTERIOR ANGLES = 360°

so if we divide 360° by 30° we find there are 12 exterior angles.

Therefore, there are 12 sides 

THUS DIAGONALS = N(N-3)/2 = 12(12-3)/2 = 12(9)/2 = 108/2 = 54 

if you find this solution helpful, do mark it as brainiest and do not forget to rate it :)