Question

Find the measures of each exterior angle of a regular Decagon

Answer 1

In a regular decagon, all sides are same size and measure of all interior angles are same.
The sum of interior angles of decagon is
$(n-2)\times {180}^o$ where $n$ is number of sides of polygon.
$(10-2)\times {180}^o={1440}^o$ here $n=10$ because deca means $10$
Each interior angle $=1440/10={144}^o$
As we know that the sum of interior and exterior angles is ${180}^o$
Exterior angle + interior angle $={180}^o$
Exterior angle $+{144}^o={180}^o$
Exterior angle $={180}^o-{144}^o={36}^o$