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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Important Questions from Lines and Angles
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
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In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
