1.

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» 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°.


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