In quadrilateral ABCD,angle A : angle B : ang | vedclass

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Question

(A) Let the angles of the quadrilateral be $x, 4x, 2x,$ and $2x$ respectively.We know that the sum of the interior angles of a quadrilateral is $360^{

Vedclass · Accepted Answer

$\angle A = 40^{\circ}, \angle B = 160^{\circ}, \angle C = 80^{\circ}, \angle D = 80^{\circ}$

Vedclass · Answer

(A) Let the angles of the quadrilateral be $x, 4x, 2x,$ and $2x$ respectively.We know that the sum of the interior angles of a quadrilateral is $360^{\circ}$.Therefore,$x + 4x + 2x + 2x = 360^{\circ}$.$9x = 360^{\circ}$.$x = 360^{\circ} / 9 = 40^{\circ}$.Now,calculating each angle:$\angle A = x = 40^{\circ}$.$\angle B = 4x = 4 	imes 40^{\circ} = 160^{\circ}$.$\angle C = 2x = 2 	imes 40^{\circ} = 80^{\circ}$.$\angle D = 2x = 2 	imes 40^{\circ} = 80^{\circ}$.Thus,the angles are $40^{\circ}, 160^{\circ}, 80^{\circ},$ and $80^{\circ}$.

In quadrilateral $ABCD$,$\angle A : \angle B : \angle C : \angle D = 1 : 4 : 2 : 2$. Find the measure of each angle of the quadrilateral.

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