Question

Find the measure of each interior angle of a regular$18$sided polygon.

Answer 1

Finding measure of interior angle:

As we know that the sum of measures of interior angles of a polygon having $n$ sides is$=(\mathrm{n}-2)\times 180\mathrm{degrees}$

The number of sides$=18$
So, the sum of measures of interior angles of decagon is $=(18-2)\times 180°=2880°$
Thus, measure of each interior angle $=\frac{\mathrm{sum}\mathrm{of}\mathrm{measures}\mathrm{of}\mathrm{interior}\mathrm{angles}}{\mathrm{total}\mathrm{no}\mathrm{of}\mathrm{sides}}$
$=\frac{2880}{18}=160°$
Hence, the measure of each interior angle is$160°$.