Question

find an angle which is two third of its complement​

Answer 1

Let the angle be x.

And its complement angle be y

By the problem x=

3

2

y

We know that,

Sum of complementary angles is 90

0

⇒y+

3

2

y=90

0

⇒

3

3y+2y

=90

0

⇒

3

5y

=90

0

⇒5y=90×3

y=

5

90×3

y=36

0

Therefore,

The angles are 54

0

,36

0

.

Answer 2

Given :

• One of the angle is ⅔ of its complement.

To Find :

• The two complementary angles.

Solution :

✰ As we know that, Two angles whose sum is 90° are called complementary angles. Therefore :

⟹ Let the First angle be x

⟹ Let it's complement angel be y

⟹ By the Question : x = ⅔ y

⠀

According to the Question :

⟼ Sum of Complements = 90°

⟼ y + 2/3 y = 90°

⟼ 3y + 2y / 3 = 90°

⟼ 3y + 2y = 90 × 3

⟼ 3y + 2y = 270

⟼ 5y = 270

⟼ y = 270 / 5

⟼ y = 54°

Therefore :

• First angle = y = 54°
• Second angle = x = ⅔y = 2/3 × 54 = 2 × 18 = 36°

Hence the Two Complementary angles are 54° and 36°

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