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The angle whose complement is one-third of its supplement is ____ $°$ .

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Detailed Solution

The angle whose complement is one-third of its supplement is 45 degree.
It is given that the complement of an angle is one-third of its supplement.
Assume the measure of an angle be x.
Complement of

.
Supplement of

.
Consider the angle x which is four times its supplement.
Therefore,

90^{o} - x = \frac{1}{3} (180^{o} - x)

By cross-multiplication,

270^{o} - 3 x = 180^{o} - x

By simplification,

270^{o} - 180^{o} = - x + 3 x

90^{o} = 2 x

x = 45^{o}

The angle is

45^{o} .

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