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Deffense [45]
2 years ago
12

Work out the size of one of the exterior angles

Mathematics
2 answers:
hodyreva [135]2 years ago
8 0

<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>

⠀

  • A polygon with 10 sides ( Decagon )

⠀

<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

⠀

  • The value of one of the exterior angles

⠀

<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

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

⠀

<u>Solution</u><u> </u><u>:</u><u>-</u>

⠀

Putting the given values, we get,

⠀

\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 \\  \\

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

⠀

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

tankabanditka [31]2 years ago
4 0

Answer:

  • 36° .

⠀

Explanation :

⠀

For a regular polygon of <em>n</em> sides, we have

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

⠀

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

⠀

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

⠀

Now, substituting the value :

⠀

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

⠀

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

⠀

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

⠀

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

⠀

Therefore,

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