Question

In a quadrilateral ABCD, the angel A,
B. C. D are in ratio 3:5:7:9. Find the
measure of the angel D of the
quadrilateral.​

Answer 1

Answer:

Let the comm9n ratio bex

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 = 3x18 = 54°(Angle B)

7x= 7x18 = 126°(Angle C)

9x= 9x18 = 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

Mark as brainliest pl.

Answer 2

Answer:

The value of D is 135 degree

$3x + 5x + 7x + 9x = 360$

$24x = 360$

$x = 360 \\ x = 15 \\ \: 3x = 45 \\ 5x = 75 \\ 7x = 105 \\ 9x = 135$

A = 45°

B = 75°

C = 105°

D = 135°

Step-by-step explanation:

the required value is 135°