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(i) If the angles of a quadrilateral are in the ratio 1:2:3:4, find the angles.
(ii) The angles of a quadrilateral are in the ratio 2 : 5:5:6. Find the greatest angle. please answer step by step
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(I)Let the measure of angles be x,2x,3x and 4x.
We know that sum of measure of all four angles is 360
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∴ x+2x+3x+4x=360
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⇒ 10x=360
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⇒ x=36
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⇒ 2x=2×36
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=72
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⇒ 3x=3×36
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=108
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⇒ 4x=4×36
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=144
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⇒ The measures of angles of quadrilateral are 36
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,72
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,108
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and 144
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⇒ We can see measure of all 4 angles are different so, the given quadrilateral is trapezium
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