Two complementary angles are such that twice the measure of one angle is equal to three times the measure of the other. The measure of the larger angle is:
$54^{o}$
Let the two complementary angles be \(a\) and \(b\), with \(a + b = 90^\circ\).
Given \(2a = 3b \Rightarrow a = \frac{3b}{2}\).
Substituting: \(\frac{3b}{2} + b = 90^\circ \Rightarrow \frac{5b}{2} = 90^\circ \Rightarrow b = 36^\circ\).
Then \(a = 90^\circ - 36^\circ = 54^\circ\).
Hence, the measure of the larger angle is 54°.
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