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Likewise, sarah assumes that value of an exterior angle of the same dodecagon is (5y+7)°, then the value of y is

User Tamie
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The sum of the interior angles of a dodecagon is:


\begin{gathered} (N-2)\cdot180\text{, where N is the number of sides} \\ For\text{ a dodecagon N=12, so:} \\ (12-2)\cdot180=1800 \end{gathered}

For a regular dodecagon the interior angles are equal, so:


\text{angle}=(1800)/(12)=150

Each interior angle in a regular dodecagon has 150°. The exterior angle is supplematery of the corresponding interior angle, so:


\begin{gathered} 150+\angle exterior=180 \\ \angle exterior=180-150=30 \end{gathered}

Sarah, assumes that the exterior angle has a value of (5y+7)°, so:


\begin{gathered} 5y+7=30 \\ 5y=30-7 \\ y=(23)/(5) \\ y=4.6 \end{gathered}

The value of y is 4.6

User Mbelsky
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