Math, asked by anushadennis, 4 months ago

(2x - 30) and (x + 60) are a pair of complementary angles.
Find the following values:
The smaller angle is :
The greater angle is :​

Answers

Answered by vkadithyan
0

Step-by-step explanation:

the smaller angle is 10 and greater angle is 80

Attachments:
Answered by TwilightShine
15

Answer :-

  • The two angles are 10° and 80°.
  • 10° is the smaller angle and 80° is the greater angle.

Given :-

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

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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