Question

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

Answer 1

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:

$\text{angle}=\frac{1800}{12}=150$

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:

$\begin{gathered} 5y+7=30 \\ 5y=30-7 \\ y=\frac{23}{5} \\ y=4.6 \end{gathered}$

The value of y is 4.6