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3 years ago

The complement of an angle is 8 times as large as the angle. find the measure of the complement

2 answers:

3 0

Complement angles means that the sum of the two angles equal to 90°.
Thus,
x + 8x = 90
9x = 90
x = 10°
8x = 80°
The complement is 80°

ss7ja [257]3 years ago

3 0

Answer:

80⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

8x = 90 - x

9x = 90

x = 10⁰

Complement = 90 - 10 = 80⁰

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$\boxed{ \bold{ \boxed{ \sf{1. \: \: \: \: \: x = 12}}}}$

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$\sf{1. \: \: \: \: \frac{x}{3} + 2 = \frac{x}{4} + 3}$

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Similarly, move 2 to right hand side and change it's sign

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$\longrightarrow{ \sf{ \frac{x \times 4 - x \times 3}{12} = 3 - 2}}$

$\longrightarrow{ \sf{ \frac{4x - 3x}{12} = 3 - 2}}$

$\longrightarrow{ \sf{ \frac{x}{12} = 3 - 2}}$

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$\longrightarrow{ \sf{ \frac{x}{12} = 1}}$

Do cross multiplication

$\longrightarrow{ \sf{x = 1 \times 12}}$

$\longrightarrow { \sf{x = 12}}$

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$\sf{2. \: \: \: \: 3(4 + 2x) = 33 - x }$

Distribute 3 through the parentheses

$\longrightarrow{ \sf{12 + 6x = 33 - x}}$

Move x to left hand side and change it's sign

Similarly, move 12 to right hand side and change it's sign

$\longrightarrow{ \sf{6x + x = 33 - 12}}$

Collect like terms

$\longrightarrow{ \sf{7x = 33 - 12}}$

Subtract 12 from 33

$\longrightarrow{ \sf{7x = 21}}$

Divide both sides by 7

$\longrightarrow{ \sf{ \frac{7x}{7} = \frac{21}{7} }}$

Calculate

$\longrightarrow{ \sf{x = 3}}$

Hope I helped!

Best regards! :D

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