Question

The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.

Answer 1

Answer:

Angles of the quadrilateral are:-

36º

60º

108º

156º

Explanation:

Given :

• The angles of quadrilateral are in the ratio3 : 5: 9: 13

To Find

• All the angles of the quadrilateral.

Solution :

Let the common ratio between the angles be x.

Therefore, the angles will be 3x, 5x, 9x, and 13x respectively.

As the sum of all interior angles of a quadrilateral is 360º,

∴ 3x + 5x + 9x + 13x = 360º

30x = 360º

x = 12º

Hence, the angles are

3x = 3 × 12 = 36º

5x = 5 × 12 = 60º

9x = 9 × 12 = 108º

13x = 13 × 12 = 156º

Answer 2

Answer:

36°,60°,108°,156°

Step-by-step explanation:

Given

The ratio of angles of quadrilateral is 3:5:9:13 .

Let the angles be 3x,5x,9x and 13x.

We know, sum of all angles of a quadrilateral = 360°

Or, 3x+5x+9x+13x= 360

Or, 30x=360

Or, x=12.

Hence ,

The angles of the quadrilateral are 36°,60°,108° and 156°.