Question

One of a pair of complementary angles, one is two - third of the other. Find the angles.
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Answer 1

★ Appropriate Question -

• Of a pair of complementary angles, one is two-third of the other. Find the angles.

★ Answer -

• The angles are 36° and 54°.

★ To find -

• The angles.

★ Step-by-step explanation -

• Let's form an equation using the information given to us and solve it to find out our answer!

Let -

• One of the angles be "x".

Then -

• The other angle will be "(2/3) x", as it is two-third of the first angle.

We know that -

$\bigstar \: \underline{ \boxed{ \sf Complementary \: angles \: add \: up \: to \: 90^{\circ}}}$

Therefore -

$\longmapsto \tt x + \dfrac{2}{3} x = 90$

$\longmapsto \tt x + \dfrac{2x}{3} = 90$

$\longmapsto \tt \dfrac{(x \times 3) + (2x \times 1)}{3} = 90$

$\longmapsto \tt\dfrac{3x + 2x}{3} = 90$

$\longmapsto \tt \dfrac{5x}{3} = 90$

$\longmapsto\tt5x = 90 \times 3$

$\longmapsto\tt5x = 270$

$\longmapsto \tt x = \cancel\dfrac{270}{5}$

$\longmapsto \underline{\boxed{\tt x = {54}^{ \circ}}}$

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Hence, the complementary angles are -

$\Rightarrow\bf x = {54}^{ \circ} .$

$\Rightarrow\bf \dfrac{2}{3} x = \dfrac{2}{3} \times 54 = {36}^{ \circ} .$

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Answer 2

Question :-

One of a pair of complementary angles, one is two - third of the other. Find the angles.

Answer :-

• The angles are 54° and 36°.

Step by step explanation :-

In the question we have said that the one pair of complementary angles one is two - third part of other. And we have asked to find the measure of angles.

Method of solving,

See here we have to assume the measures of angles and we use the property of complementary angles.

Assumption,

$\implies$ 1st angle be x.

$\implies$ 2nd angle be $\frac{2}{3}$ x.

Complementary angles property,

$\implies$ Sum of two angles of complementary angles is 90°.

On using this property,

$\rm:\longmapsto{x + \frac{2}{3} x = 90 \degree}$

Also can be written as,

$\rm:\longmapsto{x + \frac{2x}{3} = 90 \degree}$

Taking LCM,

$\rm:\longmapsto{ \frac{3x + 2x}{3} = 90 \degree} \\ \\ \rm:\longmapsto{5x = 90 \degree \times 3} \: \: \: \: \\ \\ \rm:\longmapsto{5x = 270 \degree} \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{x = \cancel \frac{270}{5} } \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto \red{x = 54 \degree} \: \: \: \: \: \: \: \: \: \: \: \:$

The angles are,

$\implies$ 1st angle = x = 54°

$\implies$ 2nd angle = $\frac{2}{3}$ x

$\rm \implies{ \frac{2x}{3} = \frac{2(54)}{3} } \\ \\ \rm \implies{ \frac{108}{3} = \red {36 \degree }} \: \: \:$

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