The angles of a quadrilateral are in the ratio 3 : 2 : 4 : 1. Find the angles. Assign a special name to the quadrilateral.

108^{\circ}, 82^{\circ}, 144^{\circ}, 36^{\circ}

, Trapezium

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108^{\circ}, 92^{\circ}, 144^{\circ}, 36^{\circ}

,Trapezium

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108^{\circ}, 72^{\circ}, 144^{\circ}, 36^{\circ}

,Trapezium

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108^{\circ}, 142^{\circ}, 144^{\circ}, 36^{\circ}

, Trapezium

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Solution

The correct option is B $108^{\circ}, 72^{\circ}, 144^{\circ}, 36^{\circ}$ ,Trapezium
$T h e r a t i o o f a n g l e s o f q u a d i l a t e r a l = 3 : 2 : 4 : 1 L e t t h e a n g l e s o f q u a d i l a t e r a l = 3 x + 2 x + 4 x + x = 360 10 x = 360, x = 36 ∴ a n g l e s o f q u a d i l a t e r a l a r e 3 x = 3 \times 36 = 108 2 x = 2 \times 36 = 72 4 x = 4 \times 36 = 144 I n t h e a d j o i n i n g f i g u r e ∠ A + ∠ B = 108 + 72 = 180 i e t h e s u m o f i n t e r i o r a n g l e s o n t h e s a m e s i d e o f t r a n s v e r s a l A B = 180 ∴ A D ∥ B C, H e n c e q u a d i l a t e r a l A B C D i s a t r a p e z i u m$

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Similar questions

16 cos 144^{0} . cos 108^{0} . cos 72^{0} . cos 36^{0} =

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a

cos 36^{0} cos 72^{0} cos 108^{0} cos 144^{0} = \frac{1}{2 a}

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