Find the measure of the angles of a quadrilateral if the angles are in the ratio $2 : 5 : 9 : 2 .$

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Solution

Let the angles be $2 x, 5 x, 9 x a n d 2 x$ .
Sum of all angles of a quadrilateral is $360 ° .$
$2 x + 5 x + 9 x + 2 x = 360 ° \Rightarrow 18 x = 360 ° \Rightarrow x = \frac{360 °}{18} = 20$
$2 x = 2 \times 20 = 40 ° 5 x = 5 \times 20 = 100 ° 9 x = 9 \times 20 = 180 ° 2 x = 2 \times 20 = 40 °$
Hence, the angles are $40 °, 100 °, 180 °, 40 ° .$

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