Two complementary angles are such that two times the measure of one is equal to three times

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is

Let one angle be x°.

Then, the other complementary angle becomes (90 - x)°

It is given that two times the angle measuring x°is equal to three times the angle measuring (90 - x)°

Or, we can say that:

2x = 3(90 - x)

2x = 270 - 3x

2x + 3x = 270

5x = 270

On dividing both sides of the equation by 5,we get

`x = 270/5`

x = 54

Also, the other complementary angle becomes

90 - x = 90 - 54

= 36

Thus, the measure of the required smaller angle is 36°.

Concept: Introduction to Lines and Angles

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Two complementary angles are such that twice the measure of the one is equal to the three times the measure of the other .the larger of the two measures

Solution

Complementary angles of the angles whose sum is equal to 90 degree Let the measure of the angle be 2x and 3x So 2X + 3 x is equal to 90 5x=90 X=90÷5 X=18 So angles are. 2×x=2×18=36° 3×x=3×18=54° So the measure of the larger angle is 54 degree
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Now, the other angle will be ${{90}^{\circ }}-x$ .We are given that two times the measure of one angle is equal to three times the measure of the other.$\Rightarrow 2x=3\left( {{90}^{\circ }}-x \right)$Let us expand the RHS. We will get$2x={{270}^{\circ }}-3x$Let us collect the variables on one side. We will get$2x+3x={{270}^{\circ }}$On adding the LHS, we will get$5x={{270}^{\circ }}$Let us find x by taking 5 from LHS to RHS. $x=\dfrac{{{270}^{\circ }}}{5}$On solving the above expression, we will get$x={{54}^{\circ }}$Now, we have to find the measure of the other angle which is \[{{90}^{\circ }}-x={{90}^{\circ }}-{{54}^{\circ }}={{36}^{\circ }}\]We got the measure of angles as ${{54}^{\circ }}\text{ and }{{36}^{\circ }}$ .We know that the largest angle is ${{54}^{\circ }}$ .Hence, the correct option is D.

So, the correct answer is “Option D”.

Note: We can also write the expression according to the given condition as

$2\left( {{90}^{\circ }}-x \right)=3x$Let us solve this.${{180}^{\circ }}-2x=3x$Let us take the variables on one side.$\begin{align} & 3x+2x={{180}^{\circ }} \\ & \Rightarrow 5x={{180}^{\circ }} \\ \end{align}$On solving the above expression, we will get$x=\dfrac{{{180}^{\circ }}}{5}={{36}^{\circ }}$Hence, the other angle is ${{90}^{\circ }}-{{36}^{\circ }}={{54}^{\circ }}$

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