The angles of a quadrilateral are in ratio 1 : 3 : 7 :9 find the measure of each angle.

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Solution

Let angles are $x^{\circ}, 3 x^{\circ}, 7 x^{\circ}, 9 x^{\circ} ∴ x + 3 x + 7 x + 9 x = 360^{\circ} \Rightarrow 20 x = 360 x = 18 ∴ a n g l e s a r e 18, 18 \times 3, 18 \times 7, 18 \times 9 = 18^{\circ}, 54^{\circ}, 126^{\circ}, 162^{\circ} V e r i f i c a t i o n 18^{\circ} + 54^{\circ} + 126^{\circ} + 162^{\circ} = 360^{\circ}$

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