Question

he angles of quadrilateral are in the ratio 7 : 3 : 2 : 6 . Find all the angles of the quadrilateral.​

Answer 1

Given :

• The angles of a quadrilateral are in the ratio 7:3:2:6

To Find :

• The angles of the quadrilateral.

Calculations :

Let's consider the angles of quadrilateral as 7x, 3x, 2x and 6x.

• 7x
• 3x
• 2x
• 6x

We know that,

• $\boxed{ \tt{ \underline{Sum \: of \: angles_{(Quadrilateral)} = 360^{\circ}}}}$

Now, putting the values,

$\mapsto \sf 7x + 3x + 2x + 6x = 360^{\circ}$

Adding the numbers,

$\mapsto \sf 18x = 360^{\circ}$

Transposing 18 to R.H.S and dividing 360° by 18,

$\mapsto \sf x = \cancel\dfrac{360^{\circ}}{18}$

On dividing,

$\mapsto \rm{ \red{x = 20}}$

• Hence, value of x is 20.

$\dag$ According to the Question,

• Now coming to the question, so as per the question we are asked to find all the angles of quadrilateral.

• Since we got the value of x, we'll perform multiplication in order to find all the angles of quadrilateral.

• We'll be multiplying the value of x [x = 20] with all the angles of quadrilateral which are in ratio [7x, 3x, 2x & 6x].

$\tiny \dag \: { \underline{ \bf{First \: angle}}}$

$\mapsto \sf 7x = 7 \times 20 \\ \\ \\ \mapsto \rm{ \pink{140^{\circ} }}$

$\tiny \dag \: { \underline{ \bf{Second \: angle}}}$

$\mapsto \sf 3x = 3 \times 20 \\ \\ \\ \mapsto \rm{ \pink{60^{\circ} }}$

$\tiny \dag \: { \underline{ \bf{Third \: angle}}}$

$\mapsto \sf 2x = 2 \times 20 \\ \\ \\ \mapsto \rm{ \pink{40^{\circ} }}$

$\tiny \dag \: { \underline{ \bf{Fourth \: angle}}}$

$\mapsto \sf 6x = 6 \times 20 \\ \\ \\ \mapsto \rm{ \pink{120^{\circ} }}$

Henceforth,

• All the angles of a quadrilateral are 140°, 60°, 40° and 120°

Answer 2

Answer :-

➪ The angles of quadrilateral are 120 Degrees , 40 Degrees , 60 Degrees , 120 Degrees .

|| To find ||

• All angles of the quadrilateral .

|| Given ||

• Ratio of the quadrilateral's angles 7 : 3 : 2 : 6

|| Solution ||

Let take the angles be

• 7a
• 3a
• 2a
• 6a

➪ 7a + 3a + 2a + 6a = 360° ( sum of the quadrilateral is 360°)

➪ 18a = 360°

➪ a = 360° ÷ 18

➪ a = 20

∴ the value of a is 20 .

_______________

where

• a = 20

➪ 1 )  7a = 7 × 20 = 140°

➪ 2) 3a = 3 × 20 = 60°

➪ 3) 2a = 2 × 20 = 40°

➪ 4) 6a = 6 × 20 = 120°

By putting the value of a we get 120° , 40° , 60° , 120° .