Question

The angles of quadrilateral are in the ratio 7 : 4 : 5 : 14. Find all the angles of the

quadrilateral.​

Answer 1

Given :

⬤ The angles ot Quadrilateral are in the Ratio 7: 4: 5: 14 .

To Find :

⬤ All the Four angles of Quadrilateral .

Solution :

Let :

• The Four angles of Quadrilateral be 7x , 4x , 5x and 14x .

Now :

As we know that , Sum of all angles of Quadrilateral is 360° . Hence ,

$\sf{7x+4x+5x+14x=360^{\circ}}$

30x = 360°

x = 360/30

x = 12

Therefore , The Value of x is 12 .

Hence ,

First Angle = 7x

= 7(12)

= 84°

Second Angle = 4x

= 4(12)

= 48°

Third Angle = 5x

= 5(12)

= 60°

Fourth Angle = 14x

= 14(12)

= 168°

Therefore , The Four angles of a Quadrilateral are 84° , 48° , 60° and 168° .

Answer 2

Question:-

The angles of quadrilateral are in the ratio 7 : 4 : 5 : 14. Find all the angles of the quadrilateral.

Answer:-

• The angles of quadrilateral are 84°,48°,60° and 168°.

Solution:-

• Ratio = 7:4:5:14

Put x in the ratio

• First angle = 7x
• Second angle = 4x
• Third angle = 5x
• Fourth angle = 14x
• Sum of angles = 360°( Angle sum property)

$\large{ \tt : \implies \: \: \: \: 7x + 4x + 5x + 14x = 360 \degree}$

$\large{ \tt : \implies \: \: \: \: 30x = 360 \degree}$

$\large{ \tt : \implies \: \: \: \: x = \frac{360}{30} }$

$\large{ \tt : \implies \: \: \: \: x = 12 \degree}$

• The value of x is 12°

________________________________

• First angle = 7x = 7×12 = 84°
• Second angle = 4x = 4×12 =48°
• Third angle = 5x = 5×12 = 60°
• Fourth angle = 14x = 14×12 = 168°

________________________________

The angles of quadrilateral are 84°,48°,60° and 168°.