Question

In the adjoining figure, show that
∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 360°.

Answer 1

In $∆ACE$ , we have :
$\angle A+\angle C+\angle E=180°...\left(i\right)$ [Sum of the angles of a triangle]
In $∆BDF$, we have :
$\angle B+\angle D+\angle F=180°...\left(ii\right)$ [Sum of the angles of a triangle]​

$$\begin{gathered} \mathrm{Adding}\left(i\right)\mathrm{and}\left(ii\right),\text{we get:} \\ \angle A+\angle C+\angle E+\angle B+\angle D+\angle F=\left(180+180\right)° \end{gathered}$$
$\Rightarrow \angle A+\angle B+\angle C+\angle D+\angle E+\angle F\mathbf{=}\mathbf{360}\mathbf{°}$