Question

each interior angle of a regular polygon is 120°, find:1) the measure of each exterior angle. 2) the number of sides of the polygon. 3) the name of the polygon.​

Answer 1

Given Question :-

Each interior angle of a regular polygon is 120°, find:

• 1) the measure of each exterior angle.
• 2) the number of sides of the polygon.
• 3) the name of the polygon.

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☆ Solution :-

$\bf \:\large \red{AηsωeR : 1.} ✍$

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$\tt \:  ⟼We \: know, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \:  \: interior \: angle \: + exterior \: angle \: = 180°$

$\tt\implies \:120° \: + \: exterior \: angle \: = 180°$

$\tt\implies \:\: exterior \: angle \: \: = 180° - 120° = 60°$

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$\bf \:\large \red{AηsωeR : 2} ✍$

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$\tt \:  ⟼ \: We \: know, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \:  number \: of \: sides \: = \dfrac{360°}{\: exterior \: angle \:}$

$\tt\implies \:number \: of \: sides \: = \dfrac{360}{60} = 6$

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$\bf \:\large \red{AηsωeR : 3} ✍$

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$\tt \:  A \: polygon \: having \: 6 \: sides \: is \: called \: hexagon$

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