Mathematics

# In the figure, show that $\angle A + \angle B + \angle C + \angle D + \angle E + \angle F = 360^{\circ}$.

##### SOLUTION
We know that the sum of all the angles in triangle $ACE$ is $180^{\circ}$.
$\angle A + \angle C + \angle E = 180^{\circ} .. (1)$
We know that the sum of all the angles in triangle $BDF$ is $180^{\circ}$.
$\angle B + \angle D + \angle F = 180^{\circ} .. (2)$
Now by adding both equations $(1)$ and $(2)$ we get
$\angle A + \angle C + \angle E + \angle B + \angle D + \angle F = 180^{\circ} + 180^{\circ}$
On further calculation
$\angle A + \angle B + \angle C + \angle D + \angle E + \angle F = 360^{\circ}$
Therefore, it is proved that $\angle A + \angle B + \angle C + \angle D + \angle E + \angle F = 360^{\circ}$.

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Subjective Medium Published on 09th 09, 2020
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