Question

What is the sum of the interior angles of a decagon?


A.


1800°


B.


1620°


C.


1440°


D.


1260°

Answer 1

The sum of the exterior angles must be \(360^\circ\), so any one exterior angle will have measure \(\dfrac{360}{10}=36^\circ\). This means any one interior angle will have measure \(180-36=144^\circ\), since interior and exterior angles are supplementary.

The sum of all the exterior angles would thus be \(10\times144^\circ=1440^\circ\).

Answer 2

thank you