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If the ratio of four angles of a quadrilateral is $∠ A : ∠ B : ∠ C : ∠ D = 1 : 2 : 3 : 4$ , what is the value of $∠ C$ ?

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$90 °$

$108 °$

$180 °$

$72 °$

answer is B.

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Detailed Solution

Let $∠ A = x$ , then $∠ B = 2 x, ∠ C = 3 x a n d ∠ D = 4 x$
We know that sum of the four angles of a quadrilateral is $360 °$
Therefore, $∠ A + ∠ B + ∠ C + ∠ D = 360 °$
$x + 2 x + 3 x + 4 x = 360 °$
$10 x = 360 °$
$x = 36 °$
Now, $∠ C = 3 x = 3 (36 °) = 108 °$

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