Question

Work out the size of one of the exterior angles

Answer 1

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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`\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \frac {360^\circ}{no. ~of~sides}}}} \: \star`

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Solution :-

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Putting the given values, we get,

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`\sf \dashrightarrow Exterior ~angle = (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 \\ \\`

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

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`\underline{ \rule{227pt}{2pt}} \\ \\`

Answer 2

• 36° .

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Explanation :

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For a regular polygon of n sides, we have

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

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

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

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

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`{\pmb{ \frak{ \longrightarrow \qquad Each \: exterior \: angle_((Decagon)) = 36^( \circ) }}}`

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Therefore,

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