In the given figure, AC, CE, EG, AG, BH, HF, FD and BD are line segments. The value of $(∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F + ∠ G + ∠ H)$ is

180^{0}

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360^{0}

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540^{0}

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720^{0}

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Solution

The correct option is D $720^{0}$
In quadrilateral ACEG, by Angle sum property,
$∠ A + ∠ C + ∠ E + ∠ G = 360 °$ …..(i)
Similarly, in quadrilateral BDFH,
$∠ B + ∠ D + ∠ F + ∠ H = 360 °$ …..(ii)
Adding (i) and (ii), we get
$∠ A + ∠ C + ∠ E + ∠ G + ∠ B + ∠ D + ∠ F + ∠ H = 360 ° + 360 °$ $\Rightarrow ∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F + ∠ G + ∠ H = 720 °$ Hence, the correct answer is option (d).

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