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Question
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.
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Solution
\[\text{ Let x be the measure of each angle } . \]
\[\text{ Then the ratio becomes x : 2x : 4x : 5x .} \]
\[ \text{ Since, the sum of all angles in a quadrilateral is } 360° , \text{ we have } : \]
\[x + 2x + 4x + 5x = 360° \]
\[ \Rightarrow 12x = 360° \]
\[ \Rightarrow x = \frac{360° }{12}\]
\[ \Rightarrow x = 30° \]
\[\text{ Thus, the angles are } : \]
\[x = 30 ° \]
\[2x = 60° \]
\[4x = 120° \]
\[5x = 150° \]
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