Question

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

Answer 1

Answer:

1. 3x+5x+9x+13x=360
2. 30x=360
3. x=12
4. angles are 36,60,108,156

Answer 2

Answer :–

• $\tt \angle1 = 36 \degree$
• $\tt \angle2 = 60 \degree$
• $\tt \angle3 = 108 \degree$
• $\tt \angle4 = 156 \degree$

Given :–

• Angles of the quadrilateral in the ratio form = 3 : 5 : 9 : 13.

To Find :–

• All the angles of the quadrilateral.

Solution :–

Let,

• The first angle be 3x.

• The second angle be 5x.

• The third angle be 9x.

• The fourth angle be 13x.

We know that,

Sum of all angles of a quadrilateral = 360°

I.e.,

↣ $\angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

So,

We have,

• $\tt \angle1 = 3x$
• $\tt \angle2 = 5x$
• $\tt \angle3 = 9x$
• $\tt \angle4 = 13x$

Now,

↣ $3x + 5x + 9x + 13x = 360 \degree$

↣ $8x + 22x = 360 \degree$

↣ $30x = 360 \degree$

↣ $x = \dfrac{ 36\cancel{0} \degree}{ 3\cancel{0}}$

↣ $x = \dfrac{ \cancel{36} \degree}{ \cancel3}$

↣ $x = 12 \degree$

So all the angles are,

• The first angle = 3x = 3 × 12° = 36°

• The second angle = 5x = 5 × 12° = 60°

• The third angle = 9x = 9 × 12° = 108°

• The fourth angle = 13x = 13 × 12° = 156°

Check :–

Sum of all angles of a quadrilateral = 360.

• $\tt \angle1 = 36 \degree$
• $\tt \angle2 = 60 \degree$
• $\tt \angle3 = 108 \degree$
• $\tt \angle4 = 156 \degree$

↣ $36 \degree + 60 \degree+ 108 \degree+ 156 \degree$

↣ $96 \degree + 264 \degree$

↣ $360 \degree$

Since, we get sum of all the angles are 360°.

So, the all angles of a quadrilateral is 36°, 60°, 108° and 156° is correct.