Question

9. The measures of the angles of a quadrilateral are in the ratio 2: 4:5: 7. Find the
measure of each of its angles​

Answer 1

Answer:

40,80,100,140 are angles of quadrilateral.

Step-by-step explanation:

2:4:5:7

Let x be the common multiple.

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

Sum of angles in a quadrilateral is 360

18x=360

x=20

∴ 2x=2×20=40,4x=4×20=80,5x=5×20=100,7x=7×20=140

40,80,100,140 are angles of quadrilateral.

Answer 2

Given :-

The measures of the angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7

Let the first angle of the quadrilateral = 2x

Second angle = 4x

Third angle = 5x

Fourth angle = 7x

We know that:

Sum of all the angles of a quadrilateral = 360°

According to the question :

→ 2x + 4x + 5x + 7x = 360°

→ 18x = 360°

→ x = 360°/18

→ x = 20°

∴ Angles of quadrilateral are :

First angle = 2x = 40°

Second angle = 4x = 80°

Third angle = 5x = 100°

Fourth angle = 7x = 140°