The angles of a quadrilateral are in the ratio 2:3:4:1. Find the measure of the smallest and greatest angle.

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Solution

$\begin{matrix} L e t t h e a n g l e s o f q u a d r i l a t e r a l b e 2 x, 3 x, 4 x, x s u m o f a l l a n g l e s o f q u a d r i l a t e r a l = 360^{\circ} x + 2 x + 3 x + 4 x = 360^{\circ} 10 x = 360^{\circ} ∴ x = 36^{\circ} t h e f o u r a n g l e s a r e x = 36^{\circ} 2 x = 2 \times 36 = 72^{\circ} 3 x = 3 \times 36 = 108^{\circ} 4 x = 4 \times 36 = 144^{\circ} H e n c e, t h e s m a l l e s t a n g l e i s 36^{\circ} a n d g r e a t e s t i s 144^{\circ} . \end{matrix}$

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