Question

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

Answer 1

Question:-

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

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. ∠1+∠2+∠3+∠4=360°

So,

We have,

• ∠1=3x

• ∠2=5x

• ∠3=9x

• ∠4=13x

Now,

↣ 3x + 5x + 9x + 13x =  360°

↣ 8x + 22 x =  360°

↣ 30x = 360°

↣ x =360/30

↣ x =36/3

↣ x=12

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°.

• ∠1 = 36°

• ∠2 = 60°

• ∠3 = 108°

• ∠4 = 156°

   

↣ 36 + 60 +108 + 156 = 360°

 

↣ 96 + 264 = 360°

↣ 360°=360°

L.H.S = R.H.S

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.

Answer 2

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

 3x+5x+9x+13x=360∘

 [sum of all angles of the quadrilateral is 360∘]

30x=360∘

 x=12∘

Hence, the angles of the quadrilateral are 3×12∘=36∘,5×12∘=60∘,9×12∘=108∘and13×12∘=156∘