If ∠ A, ∠ B, ∠ C and ∠ D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6: 4, then ABCD is a

Question

Philoid · Accepted Answer

Let the required angles be 3x, 7x, 6x and 4x

3x + 7x + 6x + 4x = 360° (Sum of angles of quadrilateral)

20x = 360°

x = 18°

Hence, angles are:

3x = 3 ⨯18° = 54°

7x = 7 ⨯ 18° = 126°

6x = 6 ⨯ 18° = 108°

4x = 4 ⨯18° = 72°

Now we can observe that, 54° + 126° = 180° and 72° + 108° = 180°

Thus, ABCD is a trapezium.

Hence option C is correct.