question_answer 4)

                Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure	Side	Angle sum
	3	\[{{180}^{\text{o}}}\]
	4	\[\begin{align}   & \,\,\,\,\,\,\,2\times {{180}^{\text{o}}} \\  & =(4-2)\times {{180}^{\text{o}}} \\ \end{align}\]
	5	\[\begin{align}   & \,\,\,\,\,\,\,3\times {{180}^{\text{o}}} \\  & =(5-2)\times {{180}^{\text{o}}} \\ \end{align}\]
	6	\[\begin{align}   & \,\,\,\,\,\,\,\,\,4\times {{180}^{\text{o}}} \\  & =(6-2)\times {{180}^{\text{o}}} \\ \end{align}\]

What can you say about the angle sum of a convex polygon with number of sides? (a) 7                                       (b) 8 (c) 10                                     (d) \[n\]

Answer:

                (a) 7 Angle sum \[=(7-2)\times {{180}^{\text{o}}}\] \[=5\times {{180}^{\text{o}}}={{900}^{\text{o}}}\] (b) 8 Angle sum \[=(8-2)\times 180{}^\circ \] \[=6\times {{180}^{\text{o}}}={{1080}^{\text{o}}}\] (c) 10 Angle sum \[=(10-2)\times 180{}^\circ \] \[=8\times 180{}^\circ ={{1440}^{o}}\] (d) \[n\] Angle sum \[=(n-2)\times 180{}^\circ \]