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Papessa [141]
1 year ago
10

If the sum of the interior angles of a regular polygon is 1620°, what is the measure of one exterior angle. Round to the nearest

tenth.
Mathematics
2 answers:
lutik1710 [3]1 year ago
6 0
<h3>Interior angles of a regular polygon</h3>

<em>A </em><em>regular polygon</em><em> is a figure in which all the sides have the same </em><em>length</em><em> that is, they are equal and all the </em><em>interior angles</em><em> are of the </em><em>same measure.</em>

<h3>The formula to calculate the interior angles of any regular polygon is:</h3><h3>( n - 2 ) 180°</h3>

<em>This </em><em>regular polygon</em><em> is a </em><em>hendecagon.</em>

A hendecagon is a polygon that has 9 equal sides.

<h3>If the sum of the interior angles is 1620°, then</h3>

( n - 2 ) 180° = 1620

<em>As a second step, we divide by 180:</em>

<h3>( n-2 ) = 1620 ➗ 180</h3>

<em>We divide</em>

<h3>n - 2 = 9</h3>

<em>We change the direction, as the sign is negative, in the change of direction it starts to add.</em>

<h3>n = 9 + 2</h3>

<em>We add both numbers.</em>

<h3>n = 11</h3>

Answer: the measure of the exterior angle of the regular polygon (hendecagon) is 11. ✅

horrorfan [7]1 year ago
3 0

\textit{sum of all interior angles in a polygon}\\\\ S =180(n-2) \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ S =1620 \end{cases}\implies 1620=180(n-2) \\\\\\ \cfrac{1620}{180}=n-2\implies 9=n-2\implies \underline{11=n} \\\\[-0.35em] ~\dotfill

\textit{sum of all exterior angles in a regular polygon}\\\\ n\theta = 360 \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{angle~in}{degrees}\\[-0.5em] \hrulefill\\ \underline{n=11} \end{cases}\implies 11\theta =360\implies \theta =\cfrac{360}{11}\implies \theta \approx 32.7^o

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