Question

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

What can you say about the angle sum of a convex polygon with the number of sides (n) = 7?

• A. ${700}^0$
• B. ${800}^0$
• C. ${900}^0$
• D. ${1000}^0$

Answer 1

Answer: (C)

$Afteranalysingthegiventableitisobservedthatwhen\left(i\right)numbreofsidesofthepolygon=3⟶sumoftheinternalangles={180}^o=(3-2)\times {180}^o\left(ii\right)numbreofsidesofthepolygon=4⟶sumoftheinternalangles={360}^o=(4-2)\times {180}^o\left(iii\right)numbreofsidesofthepolygon=5⟶sumoftheinternalangles={540}^o=(5-2)\times {180}^o\left(iv\right)numbreofsidesofthepolygon=6⟶sumoftheinternalangles={720}^o=(6-2)\times {180}^o\therefore Byinduction,itcanbeconcludedthatWhenthenumbreofsidesofthepolygon=n⟶sumoftheinternalangles=(n-2)\times {180}^o\therefore Fora7sidedpolygon\to sumoftheinternalangles=(7-2)\times {180}^o={900}^o$