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Question

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


Solution

Let the angle A, B, C and D of a quadrilateral be 3x, 7x, 6x and 4x, respectively.

We have,
Sum of all the angles of a quadrilateral = 360°
⇒ 3x + 7x + 6x + 4x = 360°
⇒ 20x = 360°
​⇒ x = 18°

Thus, ∠A = 54°
B = 126°
C = 108°
D = 72°



Now, 
BCE = 180° − 108° = 72° = ∠ADE
AD || BC

Hence, ABCD is a trapezium.

Mathematics
RD Sharma (2019)
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