What is the measure of $∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F$ in the figure given below. Given reason to your answer.

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Solution

In $△ A C E$ , By angle Sum property of triangle

$∠ A + ∠ C + ∠ E = 180^{\circ}$ ... $(1)$

In $△ B D F, ∠ B + ∠ D + ∠ F = 180^{\circ}$ ... $(2)$

Adding $(1)$ and $(2)$ , we get

$∠ A + ∠ C + ∠ E + ∠ B + ∠ D + ∠ F = 180^{\circ} + 180^{\circ}$

$∴ ∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F = 360^{\circ}$

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