Question

Find the sum of the measures all the exterior angles of a decagon.

• A. ${720}^{\circ }$
• B. ${1440}^{\circ }$
• C. ${360}^{\circ }$
• D. ${1800}^{\circ }$

Answer 1

The correct option is B ${1440}^{\circ }$

Interior angle of a decagon$=\frac{{360}^{\circ }}{10}={36}^{\circ }$

Exterior angle$={180}^{\circ }-{36}^{\circ }={144}^{\circ }$

Since there are $10$ exterior angles

Hence, sum of exterior angle$=10\times {144}^{\circ }={1440}^{\circ }$