Question

If an angle is ⅔ of its complement , find the measure of the angle .​

Answer 1

Answer :-

• The angles are 54° and 36°.

Given :-

• an angle is 2/3 of its complement.

To Find :-

• Measure of the angle.

Solution :-

Let

• The angle be x
• It's complement = 2x/3

As we know that

Sum of two complementary angles is 90°.

According to question :-

⇒ x + 2x/3 = 90

⇒ (3x + 2x)/3 = 90

⇒ 5x/3 = 90

⇒ 5x = 90 × 3

⇒ 5x = 270

⇒ x = 270/5

⇒ x = 54

Now

• The angle = x = 54°
• It's complement = 2x/3 = 2(54)/3 = 36°

Hence, the angles are 54° and 36°.

Answer 2

Answer

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Given,

• An angel is 2/3 of its complement .

To find ,

• we have to find your the measure of the angles

Now,

• let the angle be "x"
• and the complement be "2x/3"

We know that ,

• the sum of two complementary angle is 90 degree .

So,

according to your given question the equation will be :- x+2x/3 = 90°

• now solving it we get ;

$\bold{ = > x + \frac{2x}{3} = 90}$

$= > \frac{3x + 2x}{3} = 90$

$= > \frac{5x}{3} = 90$

$= > 5x = 90 \times 3$

$= > 5x = 270$

$= > x = \frac{270}{5}$

$\bold{ = > x = 54 }$

So, we found the angle (x=54°)

Now,

• its complement is
• $\frac{2x}{3} = \frac{2(54)}{3} = \frac{108}{3} = 36 \degree$

So, The angels are 54° and 36°

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