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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?

If the ratio of four angles of a quadrilateral is ∠A : ∠B : ∠C : ∠D = 1 : 2 : 3 : 4, what is the value of ∠C? Correct Answer 108°

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

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