Question

The angles of quadrilateral are in the ratio of 2:3:6:7 find the measure of each angle ?
No Spam Please​

Answer 1

Answer:

let the angles be 2x,3x,6x,7x

Now sum of all angles of quadrilateral is=360

so,, 2x+3x+6x+7x=360

18x=360

x=20

Hence .2x=2*20=40

3x=3*20=60

6x=6*20=120

7x=7*20=140

So all angle measures are 40,60,120,140

Answer 2

Answer :-

• First angle = 40°
• Second angle = 60°
• Third angle = 120°
• Fourth angle = 140°

Given :-

• Ratio of angles = 2 : 3 : 6 : 7

To Find :-  

• First angle = ?
• Second angle = ?
• Third angle = ?
• Fourth angle = ?

Explanation :-

Let the all four angles to be '2x' , '3x' , '6x' and '7x'

As we know,

• The sum of all interior angles in a quadrilateral is 360°

So, making an equation

$\rm : \: \longmapsto 2x + 3x + 6x + 7x = 360^\circ$

$\rm : \: \longmapsto 5x + 13x = 360^\circ$

$\rm : \: \longmapsto 18x = 360^\circ$

$\rm : \: \longmapsto x = \dfrac{360}{18} ^\circ$

$\blue { \bf : \: \longmapsto x = 20^\circ \quad \star}$

Now, Substituting the value of 'x'

$\rm \odot \: First \: Angle = 2x = 2(20) = \bold{40^\circ}$

$\rm \odot \: Second \: Angle = 3x = 3(20) = \bold{60^\circ}$

$\rm \odot \: Third \: Angle = 6x = 6(20) = \bold{120^\circ}$

$\rm \odot \: First \: Angle = 7x =7(20) = \bold{140^\circ}$

For Verification,

$\rm : \: \longmapsto 40^\circ + 60^\circ + 120^\circ + 140^\circ = 360^\circ$

$\rm : \: \longmapsto 100^\circ + 260^\circ = 360^\circ$

$\rm : \: \longmapsto 360^\circ = 360^\circ$

$\bf : \: \longmapsto L.H.S = R.H.S \quad \checkmark$

Hence, the all four angles of the quadrilateral are 40°, 60°, 120° and 140° receptively.