Mathematics

Mark the correct alternative of the following.
The sum of an angle and half of its complementary angle is $$75^o$$. The measure of the angle is?


ANSWER

$$60^o$$


SOLUTION
Two Angles are Complementary when they add up to $$90^0$$
Let, $$A$$ and $$B$$ be the angles.
$$\therefore \angle A+\angle B=90^0$$        
$$\therefore \angle A=90^0-\angle B$$       ...$$(1)$$
According to condition, the sum of an angle and half of its complementary angle is $$75^0$$
$$\angle A+\dfrac1{2}\angle B=75^0$$
$$\therefore 90^0-\angle B+\dfrac1{2}\angle B=75^0\\$$
$$\therefore 90^0-\dfrac1{2}\angle B=75^0\\$$
$$\therefore 90^0-75^0=\dfrac1{2}\angle B\\$$
$$\therefore 15^0=\dfrac1{2}\angle B\\$$
$$\therefore \angle B=30^0\\$$
$$\therefore \angle A=60^0$$
Therefore, measure of the required angle is $$60^0$$

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Single Correct Medium Published on 09th 09, 2020
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