Question

the angles A,B,C and D of a quadrilateral ABCD are in the ratio 2:4:5:7.
what type of a quadrilateral is it?​

Answer 1

Answer:

Step-by-step explanation:

Given :-

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

To Find :-

Type of a quadrilateral

Solution  :-

Let the angles of Quadrilateral ABCD be 2x, 4x, 5x and 7x

According to the Question

⇒ 2x + 4x + 5x + 7x = 360°

⇒ 18x = 360°

⇒ x = 360°/18

⇒ x = 20°

The angles are A = 40°, B = 80°, C = 100° and 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.

Answer 2

Answer:

Step-by-step explanation:

Given :-

Ratio of Quad ABCD = 2:4:5:7

Solution :-

Let the angles be 2x, 4x, 5x and 7x.

The sum of angles of a quadrilateral is 360°

⇒ 2x + 4x + 5x+ 7x = 360°

⇒ 18x = 360°

⇒ x = 360/18

⇒ x = 20°

2x ⇒ 2×20 = 40°

4x ⇒ 4× 20 = 80°

5x ⇒ 5× 20 = 100°

7x ⇒ 7× 20 = 140°

Hence, The sum of two sides is equal to sum of other two side.

Hence, It is Trapezium.