Question

in quadrilateral ABCD if,A:B:C:D = 3:2:4:5 then identify the ABCD

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Answer 1

Correct Question :-

• In a quadrilateral ABCD are vertex if, A : B : C : D (Angles)  = 2 : 3 : 6 : 7 then identify the angles A,B,C & D .

Answer :-

• Angle A = 40°
• Angle B = 60°
• Angle C = 120°
• Angle D = 140°

Given :-

• Ratio of all angles = 2 : 3 : 6 : 7

To Find :-

• Angle A = ?
• Angle B = ?
• Angle C = ?
• Angle D = ?

Explanation :-

Let the all four angles (A,B,C,D) of the quadrilateral to be 2x, 3x, 6x and 7x respectively.

As we know,

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

So making an equation,

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

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

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

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

$\green { \boxed { \sf : \: \longmapsto \bold{x = 20^\circ} }}$

Now, substituting the value of 'x'

$\sf \star \; Angle \: A = 2x = 2(20) = \bold{\red{40^\circ}}$

$\sf \star \; Angle \: B = 2x = 3(20) = \bold{\red{60^\circ}}$

$\sf \star \; Angle \: C = 6x = 6(20) = \bold{\red{120^\circ}}$

$\sf \star \; Angle \: C = 7x = 7(20) = \bold{\red{140^\circ}}$

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