If angles A, B, C and D of the quadrilateral ABCD, taken in order, are

1.	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(A) rhombus(B) parallelogram(C) trapezium(D) kite
Answer» (C) trapezium Explanation: As angle A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3: 7: 6: 4, We have the angles A, B, C and D = 3x, 7x, 6x and 4x. Now, sum of the angle of a quadrilateral = 360^o. 3x + 7x + 6x + 4x = 360^o ⇒20x = 360^o ⇒ x = 360 ÷ 20 =18^o So, the angles A, B, C and D of quadrilateral ABCD are, ∠A = 3×18^o= 54^o, ∠B = 7×18^o = 126^o ∠C = 6×18^o = 108^o ∠D = 4×18^o = 72^o AD and BC are two lines cut by a transversal CD Now, sum of angles ∠C and ∠D on the same side of transversal, ∠C +∠D =108^o + 72^o =180 Hence, AD\|\| BC So, ABCD is a quadrilateral in which one pair of opposite sides are parallel. Hence, ABCD is a trapezium. Therefore, option (C) is the correct answer.

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(A) rhombus(B) parallelogram(C) trapezium(D) kite

Answer»

(C) trapezium

Explanation:

As angle A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3: 7: 6: 4,

We have the angles A, B, C and D = 3x, 7x, 6x and 4x.

Now, sum of the angle of a quadrilateral = 360^o.

3x + 7x + 6x + 4x = 360^o

⇒20x = 360^o

⇒ x = 360 ÷ 20 =18^o

So, the angles A, B, C and D of quadrilateral ABCD are,

∠A = 3×18^o= 54^o,

∠B = 7×18^o = 126^o

∠C = 6×18^o = 108^o

∠D = 4×18^o = 72^o

AD and BC are two lines cut by a transversal CD

Now, sum of angles ∠C and ∠D on the same side of transversal,

∠C +∠D =108^o + 72^o =180

Hence, AD|| BC

So, ABCD is a quadrilateral in which one pair of opposite sides are parallel.

Hence, ABCD is a trapezium.

Therefore, option (C) is the correct answer.

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