Question

What is the value of $\angle$A + $\angle$B + $\angle$C + $\angle$D + $\angle$E + $\angle$F ?

• A. 150${}^{\circ }$
• B. 180${}^{\circ }$
• C. 270${}^{\circ }$
• D. 360${}^{\circ }$

Answer 1

The correct option is D 360${}^{\circ }$

By using Legendre's theorem in $△$ACE, we have
$\angle$A + $\angle$C + $\angle$E = 180${}^{\circ }$......(i)
Similarly, using Legendre's axiom in $△$BDF, we have
$\angle$B + $\angle$D + $\angle$F = 180${}^{\circ }$......(ii)

Adding (i) and (ii), we get
$\angle$A + $\angle$B + $\angle$C + $\angle$D + $\angle$E + $\angle$F = 180${}^{\circ }$ + 180${}^{\circ }$
$\Rightarrow$ $\angle$A + $\angle$B + $\angle$C + $\angle$D + $\angle$E + $\angle$F = 360${}^{\circ }$