Question

Two complementary angles differ by 12. Find the angles.​

Answer 1

Answer :-

• The complementary angles are 39° and 51°.

Given :-

• Two complementary angles differ by 12.

To find :-

• The angles.

Step-by-step explanation :-

• Let one of the complementary angles be x.

• These complementary angles differ by 12. So let the other angle be x + 12.

• We know that complementary angles add up to 90°. So the sum of these angles must be equal to 90°.

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$\sf \longmapsto x + (x + 12) = 90^{\circ}$

Removing the brackets,

$\sf \longmapsto x + x+ 12 = 90^{\circ}$

Adding the variables,

$\longmapsto \sf 2x + 12 = 90^{\circ}$

Transposing 12 from LHS to RHS, changing it's sign,

$\sf \longmapsto 2x = 90^{\circ} - 12$

Subtracting 12 from 90°,

$\sf \longmapsto 2x = 78^{\circ}$

Transposing 2 from LHS to RHS, changing it's sign,

$\sf \longmapsto x = \dfrac{\:\:78^{\circ}}{2}$

Dividing 78° by 2,

$\longmapsto\underline{\boxed{ \sf x = 39^{\circ}}}$

• The value of x is 39°.

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Hence, both the angles are as follows :-

$\bf x = 39^{\circ}$

$\bf x + 12 = 39^{\circ} + 12 = 51^{\circ}$

Answer 2

Given :

• Two complementary angles differ by 12.
• Both angles are complementary.

To Find :

• The Angles

Solution :

✰ As that angles are complementary angles , so this means that their sum must be equal to 90°.

⟶ Let 1st angle be x

⟶ Then 2nd angle will be x + 12

According to the Question :

⟹ 1st angle + 2nd angle = 90°

⟹ x + ( x + 12 ) = 90°

⟹ x + x + 12 = 90°

⟹ 2x + 12 = 90°

⟹ 2x = 90° - 12°

⟹ 2x = 78°

⟹ x = 78° / 2

⟹ x = 39°

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Verification :

➟ 1st angle + 2nd angle = 90°

➟ x + ( x + 12 ) = 90°

➟ x + x + 12 = 90°

➟ 39 + 39 + 12 = 90°

➟ 39 + 51 = 90°

➟ 90° = 90°

Hence Verified

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Therefore :

• 1st angle = x = 39°
• 2nd angle = x + 12 = 39 + 12 = 51°

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