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29-10-2022
Mathematics

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How many sides does a regular polygon have if each interior angle measures 162 degrees.

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WhelanA185105 WhelanA185105

29-10-2022

The number of sides of the polygon is denoted by n

.Then we have the relation

[tex](n-2)\times180=162n[/tex]

On solving this,

[tex]180n-360=162n[/tex]

Then,

[tex]\begin{gathered} 180n-162n=360 \\ 18n=360 \\ n=\frac{360}{18} \\ n=20 \end{gathered}[/tex]

Hence the number of sides is 20.

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