If one angle of a parallelogram is $24^{\circ}$ less than twice its adjacent angle, then the largest angle of the parallelogram is

Let one angle of the parallelogram be $x$.

Since one angle is $24°$ less than twice its adjacent angle, the adjacent angle is $2x - 24°$.

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In a parallelogram, adjacent angles are supplementary:

$x + (2x - 24°) = 180°$

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$3x - 24° = 180°$

$3x = 204°$

$x = 68°$

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The two angles are:

First angle $= 68°$

Second angle $= 2(68°) - 24°$

$= 136° - 24°$

$= 112°$

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In a parallelogram, opposite angles are equal:

Two angles of $68°$

Two angles of $112°$

Therefore, the largest angle is $112°$.