Mathematics

How many degrees are there in an angle which equals two-third of its complement?


ANSWER

$$36^{\circ}$$


SOLUTION
Given, an angle is equal to two-third of its compliment.
Let that angle be $$A$$.
Therefore, $$\angle A = \dfrac {2}{3} (90 - \angle A)$$
$$\Rightarrow 3\angle A = 180 - 2\angle A$$
$$\Rightarrow 5\angle A = 180$$
$$\Rightarrow \angle A = 36^{\circ}$$
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