Question

The angle a, b, c and d of a quadrilateral abcd are in the ratio 2:4:5:7. What type of quadrilateral is it

Answer 1

Answer:

angles of a quadrilateral=

2x+4x+5x+7x=360

sum of angles=2x+4x+5x+7x=18x

360=18x

x=360/18

x=20

2x= 40,4x=80,5x=100,7x=140

Now,

2x+7x=40+140=180

And 4x+5x=80+100=180

Therefore it is a trapezium ...since sum of co-int. Angle is 180..

Answer 2

Answer:

Given that :-

Ratio of angles of Quadrilateral ABCD = 2:4:5:7.

To find :-

Type of a quadrilateral = ?

$\huge{\sf{\boxed{\boxed{Solution:-}}}}$

Let the angles of Quadrilateral ABCD be :-

=> 2x, 4x, 5x and 7x

A.T.Q

⇒ 2x + 4x + 5x + 7x = 360°

⇒ 18x = 360°

⇒ x = 360°/18

⇒ x = 20°

The angles are:-

A = 40°

B = 80°

C = 100°

D = 140°

A + D = 40° + 140° = 180°

B + C = 80° + 100° = 180°

Hence, ABCD is a trapezium with AB parallel to CD.

Hence,

Its a Trapezium.