Question

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

Answer:

54° and 36°

Step-by-step explanation:

Two angles are called complementary angles when their sum is equal to 90°.

Let the 2 angles be x and 90-x..

Given that one angle is two third of the other.. So the angles are x and 2x/3 (let).

Therefore,

x+2x/3 = 90°

5x/3=90°

5x = 90 × 3

5x = 270

x = 270/5

x = 54

90°-x= 90°-54°= 36°

Therefore the two angles are 54° and 36°.

Answer 2

Answer:

The angles are :

• 54° & 36°

Step-by-step explanation:

Given that, two complementary angles are such that one of them is ⅔ of the other. Find the the angles.

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Step 1 :

Let's assume the angles :

• $x \degree$

Since, another angle is ⅔ of ${x \degree}{}$

So, another angle will be :

• $\frac{2x \degree}{3}$

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Step 2 :

• Any complementary angle sums to 90°

So, we can say that,

$\implies x \degree + \frac{2x \degree}{3} = 180 \degree$

$\implies \frac{3x\degree + 2x\degree }{3} = 90 \degree$

$\implies \frac{5x\degree}{3} = 90 \degree$

$\implies x\degree = \frac{90 \times 3}{5}$

$\implies x \degree = {54\degree}{}$

One angle is 54°

Hence, another will be :

→ 90° - 54°

• [ ∵ Complementary angles = 90°]

→ 36° ✔

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