Question

The measure of angel A B C D of quadrilateral ABCD are in ratio 1:3:7:9.Find find the measure of each angle ABCD is a trapezium why ABCD is a parallelogram why

Answer 1

Answer:

Step-by-step explanation:

Let the comm9n ratio be x

Thus the angles are x, 3x,7x,9x

By angle sum property of a quadrilateral

x + 3x + 7x + 9x = 360

20x ,= 360

x = 360/30 = 18

So the angles are

x = 18° (angle A)

3x = 3×18 = 54°(Angle B)

7x= 7×18 = 126°(Angle C)

9x= 9×18 = 162° (Angle D)

Now in the quadrilateral ABCD

angle B + angle C = 54° + 126 ° = 180°

angle D + angle A = 162°+18° =180°

Hence we can say that side BC is parallel to AD ( if two parallel lines are cut by a transversal then co interior angles are supplementary)

Thus ABCD is a quadrilateral with one pair of parallel sides. Hence it is a trapezium.

ABCD is not a parallelogram since the opposite angles of this quadrilateral are not equal.

Hope it is clear

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