Question

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

Answer 1

Angles of quadrilateral are 36°, 60°, 108° and 156°.

Step-by-step explanation :

Given:-

• Angles of quadrilateral are in ratio of 3:5:9:13.

To find:-

• All angles of quadrilateral.

Solution:-

Let angles of quadrilateral be 3x, 5x, 9x and 13x.

We know that,

Sum of all angles of quadrilateral is 360°.

So,

➝ 3x + 5x + 9x + 13x = 360°

➝ 30x = 360°

➝ x = 360°/30

➝ x = 12°

Verification:-

➝ 3x + 5x + 9x + 13x = 360°

• Put x = 12°

➝ (3×12)° + (5×12)° + (9×12)° + (13×12)° = 360°

➝ 36° + 60° + 108° + 156° = 360°

➝ 360° = 360°

Hence, Verified.

3x = 3×12 = 36°

5x = 5×12 = 60°

9x = 9×12 = 108°

13x = 13×12 = 156°

Therefore,

Angles of quadrilateral are 36°, 60°, 108° and 156°.