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

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Solution

In $∆ A C E$ , we have :
$∠ A + ∠ C + ∠ E = 180 ° . . . (i)$ [Sum of the angles of a triangle]
In $∆ B D F$ , we have :
$∠ B + ∠ D + ∠ F = 180 ° . . . (i i)$ [Sum of the angles of a triangle]

$Adding (i) and (i i), we get: ∠ A + ∠ C + ∠ E + ∠ B + ∠ D + ∠ F = (180 + 180) °$
$\Rightarrow ∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F = 360 °$

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