Respuesta :

Answer:

  • 36° .

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Explanation :

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For a regular polygon of n sides, we have

[tex]\bf \longrightarrow \qquad Each \: exterior \: angle = { \bigg( {\dfrac{360}{n} } \bigg)}^{ \circ} [/tex]

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Here, We are to find the measure of each exterior ange of a regular decagon.

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  • So, we know a regular decagon has 10 sides, so n = 10 .

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Now, substituting the value :

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[tex]\sf \longrightarrow \qquad Each \: exterior \: angle_{(Decagon)} = { \bigg( {\dfrac{360}{10} } \bigg)}^{ \circ} [/tex]

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[tex]\sf \longrightarrow \qquad Each \: exterior \: angle _{(Decagon)}= { \bigg( {\dfrac{36 \cancel0}{1 \cancel0} } \bigg)}^{ \circ} [/tex]

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[tex]\sf \longrightarrow \qquad Each \: exterior \: angle_{(Decagon)} = { \bigg( {\dfrac{36}{1} } \bigg)}^{ \circ} [/tex]

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[tex] \pmb{\bf \longrightarrow \qquad Each \: exterior \: angle_{(Decagon)} = 36^{ \circ} }[/tex]

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Therefore,

  • The measure of each exterior angle of a regular decagon is 36° .
tv98tpyjzz

Answer:

It is 36 degrees because the out side is equal to 360 degrees

If you divide that by ten you get 36 for each angle

Step-by-step explanation:

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