The angles of a quadrilateral are in the rati | vedclass

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(B) The sum of the angles of a quadrilateral is $360^{\circ}$.Let the angles be $2x, 4x, 7x,$ and $5x$.$2x + 4x + 7x + 5x = 18x = 360^{\circ}$.$x = 36

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) The sum of the angles of a quadrilateral is $360^{\circ}$.Let the angles be $2x, 4x, 7x,$ and $5x$.$2x + 4x + 7x + 5x = 18x = 360^{\circ}$.$x = 360^{\circ} / 18 = 20^{\circ}$.The smallest angle of the quadrilateral is $2x = 2 	imes 20^{\circ} = 40^{\circ}$.Since the smallest angle of the triangle is equal to the smallest angle of the quadrilateral,the smallest angle of the triangle is $40^{\circ}$.Another angle of the triangle is twice the smallest angle,which is $2 	imes 40^{\circ} = 80^{\circ}$.The sum of the angles of a triangle is $180^{\circ}$.The third angle is $180^{\circ} - (40^{\circ} + 80^{\circ}) = 180^{\circ} - 120^{\circ} = 60^{\circ}$.The angles of the triangle are $40^{\circ}, 60^{\circ},$ and $80^{\circ}$.The second largest angle of the triangle is $60^{\circ}$.

The angles of a quadrilateral are in the ratio of $2: 4: 7: 5$. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle? (in $^o$)

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