Question

Each interior angle of a regular decagon is :

• A. $124°$
• B. $120°$
• C. $144°$
• D. $140°$

Answer 1

The correct option is C

$144°$

Finding the measure of each interior angle of a regular decagon

A polygon with $10$ sides is known as decagon

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

For decagon, the number of sides$=10$

So, the sum of measures of interior angles of decagon is $=(10-2)\times 180=1440°$

Now,

$\mathrm{The}\mathrm{measure}\mathrm{of}\mathrm{each}\mathrm{interior}\mathrm{angle}=\mathrm{sum}\mathrm{of}\mathrm{measures}\mathrm{of}\mathrm{interior}\mathrm{angles}÷\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{sides}$

Interior angle$=\frac{1440}{10}=144°$

Therefore, the measure of each interior angle of regular decagon is$144°$.

Hence, option (C) is the correct answer.