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Work out the size of one of the exterior angles

Work Out The Size Of One Of The Exterior Angles class=

Sagot :

Scarling

Given Information :-

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  • A polygon with 10 sides ( Decagon )

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To Find :-

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  • The value of one of the exterior angles

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Formula Used :-

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[tex] \qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star[/tex]

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Solution :-

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Putting the given values, we get,

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[tex]\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\ [/tex]

Thus, the value of the exterior angles of a Decagon is 36°.

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[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]

Answer:

  • 36° .

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Explanation :

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For a regular polygon of n sides, we have

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

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Here, We are to find the measure of each exterior angle 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{ \frak{ \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° .
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