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Question

Two angles are complementary. The larger angle is 3 less than twice the measure of the smaller angle. Find the measure of each angle.

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Solution

We know, two angles are said to be complementary, if the sum of their measures is 90.
Let x be the measure larger angle and y be the measure of smaller angle.
According to the given condition, x=2y3...(i)
We know, x+y=90,...(ii)
Substituting the value of x from (i) in (ii),, we get,
2y3+y=90
3y=93
y=31.
x=2(31)3 =623=59.
Hence, the smaller angle is 31 and the larger angle is 59.

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