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I cant seem to find the angles here any suggestions ?

A quadrilateral has angles in the ratio 1:2:3 and a fourth angle that is 31 degrees larger than the smallest angle.What is the difference in degree between the middle two angles ?

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Let x be the degrees of the smallest angle; then the angles have degrees x, 2x, 3x, and x+31. The sum of these is 360; so 7x+31=360. x=(360-31)/7 = 47. So, the angles are 47, 94, 141, and 78. The middle two values of degrees are 78 and 94, so the difference is 16 degrees. – Don Laackman Jul 7 '12 at 23:41
up vote 3 down vote accepted

The angles in the quadrilateral sum to $360^\circ$. Let the smallest angle be $x^\circ$. Solve for $x$ using $x+2x+3x+x+31=360$.

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Hint: The angles of a quadrilateral sum to $360^\circ$. If $x$ is the smallest angle, can you write an expression for each of the others? Then add them up and set the sum equal to 360.

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