In the following figure, the sum of the angles at the vertices is equal to

3 π

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2 π

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4 π

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16 π

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Solution

The correct option is B $2 π$

In given figure, contain 6 vertices A, D, B, F, C, E.
Consider $△$ ABC and $△$ EFD
We know that sum interior angles of is 180 $^{\circ}$ .
So,
$\Rightarrow$ $∠$ A + $∠$ B + $∠$ C = 180 $^{\circ}$ ---- (1)
$\Rightarrow$ $∠$ E + $∠$ F + $∠$ D = 180 $^{\circ}$ --- (2)
$S u m o f 6 a n g l e s a t v e r t i c e s = S u m o f i n t e r i o r a n g l e s o f △ A B C + S u m o f i n t e r i o r a n g l e s o f △ E F D$
From (1) and (2),
Sum of 6 angles at vertices = 180 $^{\circ}$ + 180 $^{\circ}$
$∴$ Sum of 6 angles at vertices = 360 $^{\circ}$
Converting angle into radians we get,
Sum of 6 angles at vertices is equal to $2 π$ .

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