Mathematics

Mark the correct alternative of the following.
Two complementary angles are in the ratio $$2:3$$. The measure of the larger angle is?


ANSWER

$$54^o$$


SOLUTION
Two Angles are Complementary when they add up to $$90^0$$
Let, $$A$$ be smaller angle and $$B$$ be larger angle.
$$\therefore \angle A+\angle B=90^0$$        ...$$(1)$$
According to condition, 
$$\dfrac{\angle A}{\angle B}=\dfrac2{3}\\$$
$$\therefore \angle A=\dfrac2{3}\angle B\\$$
putting this in equation $$(1)$$
$$\dfrac2{3}\angle B+\angle B=90^0\\$$
$$\therefore \dfrac5{3}\angle B=90^0\\$$
$$\therefore \angle B=54^0\\$$
$$\therefore$$ The measure of bigger angle is $$54^0$$
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Single Correct Medium Published on 09th 09, 2020
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