126°
Let the two supplementary angles be \(3x\) and \(7x\).
Since the angles are supplementary, their sum is 180°:
\(3x + 7x = 180°\)
\(10x = 180°\)
\(x = \frac{180°}{10} = 18°\)
The measures of the two angles are:
\(3x = 3(18°) = 54°\)
\(7x = 7(18°) = 126°\)
The greater of the two angles is \(126°\).
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