Mathematics

Mark the correct alternative of the following.
The sum of an angle and one third of its supplementary angle is $$90^o$$. The measure of the angle is?


ANSWER

$$45^o$$


SOLUTION
Let, required angle be $$A$$ and its supplementary angle be $$B$$.
$$\therefore \angle A+\angle B=180^0$$
$$\therefore \angle B=180^0-\angle A$$
According to condition, the sum of an angle and one third of its supplementary angle is $$90^0$$
$$\angle A+\dfrac{1}3\angle B=90^0\\$$
$$\angle A+\dfrac{1}3(180^0-\angle A)=90^0\\$$
$$\dfrac2{3}\angle A+60^0=90^0\\$$
$$\dfrac2{3}\angle A=30^0\\$$
$$\angle A=45^0\\$$
$$\therefore$$ measure of a required angle is $$45^0$$

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