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The sum of four angles of quadrilateral is equal to __________

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$360 °$

$270 °$

$90 °$

$180 °$

answer is B.

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Detailed Solution

Let’s take a quadrilateral as shown in figure. By dividing it diagonally, we can see that it breaks into two triangles.

We know that sum of three angles of any triangle is equal to $180 ° .$
Hence, $∠ Q P R + ∠ Q + ∠ Q R P = 180 ° a n d ∠ S P R + ∠ S + ∠ P R S = 180 ° .$
Now to get the sum of four angles of quadrilateral,
$∠ P + ∠ Q + ∠ R + ∠ S = (∠ Q P R + ∠ S P R) + ∠ Q + (∠ Q R P + ∠ P R S) + ∠ S$
$= (∠ Q P R + ∠ Q + ∠ Q R P) + (∠ S P R + ∠ S + ∠ P R S)$
$= 180 ° + 180 °$
$= 360 °$

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