Question

The difference between an angle and its complement is 10° find measure

of larger angle. ​

Answer 1

Answer :-

• The measure of the larger angle is 50°.

Given :-

• The difference between an angle and it's complement is 10°.

To find :-

• The measure of the larger angle.

Step-by-step explanation :-

• Let one of the numbers be x.
• The difference between the angles is 10°, so the other number will be x + 10°.
• The angles are complementary, because only complementary angles have complements.

We know that :-

$\underline{\boxed{\sf Complementary \: angles \:add\: up \:to \:90^{\circ}}}$

• So the sum of x and x + 10° must be equal to 90°.

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$\sf x + x + 10^{\circ} = 90^{\circ}$

Adding the variables,

$\sf 2x + 10^{\circ} = 90^{\circ}$

Transposing 10° from LHS to RHS, changing it's sign,

$\sf 2x = 90^{\circ} - 10^{\circ}$

Subtracting 10° from 90°,

$\sf 2x = 80^{\circ}$

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

$\sf x = \dfrac{\:80^{\circ}}{2}$

Dividing 80° by 2,

$\sf x = 40^{\circ}$

-----------------

Hence, both the angles are as follows :-

$\rm x = 40^{\circ}$

$\rm x + 10^{\circ} = 40^{\circ} + 10^{\circ} = 50^{\circ}$

It is clear that :-

• 50° is larger than 40°.
• So the measure of the larger angle is 50°.

Answer 2

Given :

• The difference between an angle and its complement is 10°
• Both the angles are complementary angles.

To Find :

• The Measure of Larger angle.

Solution :

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

⟹ Let the Smaller angle be x

⟹ Then Larger angle will be x + 10

⠀⠀

According to the Question :

⠀⠀⟼⠀⠀ Sum of Complements = 90°

⠀⠀⟼⠀⠀ x + (x + 10) = 90°

⠀⠀⟼⠀⠀ x + x + 10 = 90°

⠀⠀⟼⠀⠀ x + x = 90° - 10°

⠀⠀⟼⠀⠀ x + x = 80°

⠀⠀⟼⠀⠀ 2x = 80°

⠀⠀⟼⠀⠀ x = 80° / 2

⠀⠀⟼⠀⠀ x = 40°

⠀⠀

Therefore :

• Smaller angle = x = 40°
• Larger angle = x + 10° = 40 + 10 = 50°

Hence the Two Complementary angles are 40° and 50° and second angle is Larger by 10°

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