Question

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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Answer 1

Step-by-step explanation:

$number \: of \: side = \frac{360}{24} \\ = 15$

Answer 2

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