Question

Find the measure of angles.

1. Sum of interior angles of polygon with 4 sides ______

2. Sum of int. angles of polygon with 8 sides. ________

3. Sum of int. angles of polygon with n sides ____

4. Sum of int. angles of a polygon with 8 sides ___________

5. Each exterior angle of a regular polygon of 10 sides ________

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{polygon}\mathrm{with}\mathrm{n}\mathrm{sides}\mathrm{is}\left(\mathrm{n}-2\right){180}^{\circ }. \\ \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{polygon}\mathrm{with}4\mathrm{sides}=\left(4-2\right){180}^{\circ }=2\times {180}^{\circ }={360}^{\circ } \\ \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{polygon}\mathrm{with}8\mathrm{sides}=\left(8-2\right){180}^{\circ }=6\times {180}^{\circ }={1080}^{\circ } \\ \mathrm{Also},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{polygon}\mathrm{with}10\mathrm{sides}=\left(10-2\right){180}^{\circ }=8\times {180}^{\circ }={1440}^{\circ }. \\ \mathrm{As},\mathrm{all}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{polygon}\mathrm{have}\mathrm{same}\mathrm{measure},\mathrm{then}\mathrm{each}\mathrm{interior}\mathrm{angle}\mathrm{of}\mathrm{this} \\ 10\mathrm{sided}\mathrm{polygon}=\frac{1440}{10}={144}^{\circ }. \\ \mathrm{Now},\mathrm{each}\mathrm{exterior}\mathrm{angle}\mathrm{is}\mathrm{supplementary}\mathrm{to}\mathrm{the}\mathrm{interior}\mathrm{angle},\mathrm{therefore}\mathrm{each}\mathrm{exterior}\mathrm{angle}\mathrm{will}\mathrm{be} \\ \left({180}^{\circ }-{144}^{\circ }\right)={36}^{\circ }. \end{gathered}$$