Question

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

(a) 90°

(b) 108°

(c) 180°

(d) 72°

I had been asked this question in unit test.

The doubt is from Another Condition for a Quadrilateral to be a Parallelogram in division Quadrilaterals of Mathematics – Class 9

Answer 1

Correct answer is (b) 108°

To elaborate: 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°.