Math, asked by keerthanasatheesh113, 1 month ago

(2x - 30)° and (x + 60)° are a pair of complementary angles.
Find the following values :

x =
°
The smaller angle is :
°.
The greater angle is :

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Answers

Answered by pranilchipkar
1

Answer:

The value of x is 20°. (2x - 30)° = 2° × 20° - 30° = 40° - 30° = 10°. (x + 60)° = 20° + 60° = 80°. Thus, the smaller angle is 10° and the greater angle is 80°.

Step-by-step explanation:

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Answered by kamalhajare543
25

Answer:

Answer :-

The two angles are 10° and 80°.

10° is the smaller angle and 80° is the greater angle.

 \sf\pink{Given :-}

  • (2x - 30)° and (x + 60)° are a pair of complementary angles.

  \sf \red{To  \: find :-}

  • The smaller and
  • the greater angle.

Step-by-step explanation :-

Two complementary angles are (2x - 30)° and (x + 60)°.

We know that complementary angles add up to 90°.

So, if we add these two angles, they must be equal to 90°.

Therefore, we get :-

\sf (2x - 30)^{\circ} + (x + 60)^{\circ} = 90^{\circ}

Removing the brackets,

\sf 2x^{\circ} - 30^{\circ} + x^{\circ} + 60^{\circ} = 90^{\circ}

Putting the constants and variables separately,

(- 30 + 60 = 30)

\sf 2x^{\circ} + x^{\circ} - 30^{\circ} + 60^{\circ} = 90^{\circ}

On simplifying,

\sf 3x^{\circ} + 30^{\circ} = 90^{\circ}

Transposing 30 from LHS to RHS, changing its sign,

\sf 3x^{\circ} = 90^{\circ} - 30^{\circ}

Subtracting,

\sf 3x^{\circ} = 60^{\circ}

Transposing 3 from LHS to RHS, changing its sign,

\sf x^{\circ} = \dfrac{60^{\circ}}{3}

Dividing 60 by 3,

\sf x^{\circ} = 20^{\circ}

The value of x is 20°.

So, the value of the angles are as follows :-

(2x - 30)° = 2° × 20° - 30° = 40° - 30° = 10°.

(x + 60)° = 20° + 60° = 80°.

Thus, the smaller angle is 10° and the greater angle is 80°.

Verification :-

To check our answer, lets add these two angles and see whether they add up to 90°.

80° + 10° = 90°.

Since they add up to 90°.

Hence verified!

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