Question

the angle of a quadrilateral are in ratio 2:4:5:7 . find the angles.

Answer 1

Our given ratio of angles is 2:4:5:7. Let common multiplying factor be x°.
Hence, ∠A = 2x°, ∠B = 4x°, ∠C = 5x° and∠D = 7x°
Since the sum of the angles of a quadrilateral is 360°, we have:
∴ 2x + 4x + 5x + 7x = 360°
∴ 18 x = 360° ​
∴ x = 20°
∴ ∠A = 40°; ∠B = 80°; ∠C = 100°; ∠D = 140°
Hence, the measure of the angles are 40°, 80°, 100° and 140°

Answer 2

Let the four angles of the quadrilateral be 2x, 4x, 5x and 7x respectively.

We know the sum of them is 360°

So, we will simply add the all the angles we took and will equal to 360.

We will get the value of x

Finally, we will subsitute the values

→ 2x + 4x + 5x + 7x = 360

→ 6x + 5x + 7x = 360

→ 11x + 7x = 360

→ 18x = 360

→ x = 360/18

→ x = 20

Thus, we for got the value of x as 20

We will subsitute the values :-

2x = 2 × 20 = 40°

4x = 4 × 20 = 80°

5x = 5 × 20 = 100°

7x = 7 × 20 = 140°

Hence, done