The sum of the interior angles of a polygon is three times the sum of its exterior angles.

Question:

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.

Solution:

$\left\{(2 \mathrm{n}-4) \times 90^{\circ}\right\}=3 \times\left(\frac{360^{\circ}}{\mathrm{n}} \times \mathrm{n}\right)$

$\Rightarrow(\mathrm{n}-2) \times 180=3 \times 360$

$\Rightarrow \mathrm{n}-2=6

$\therefore \mathrm{n}=8$

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