i) Find the number of sides of a regular polygon if the measure of :
a) an exterior angle is 24
b) each interior angle is165
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Step-by-step explanation:
Answered by
1
Step-by-step explanation:
[a]
Sum of exterior angle of polygon = 360°
Each exterior angle of polygon = 24°
Number of sides of polygon = 360/24
⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀ = 15
[b]
Interior angle of given polygon = 165°
Exterior angle of polygon = 180° −165° = 15°
The sum of exterior angles of any polygon is 360°
Number of sides of regular polygon = 360/15
⠀⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀⠀⠀ = 24
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