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An angle is twice as large as its complement, what is the measure of the angle and its complement?

Answer 1

Sadie Allen

An angle and its complement add up to #90^@#

This means we have #x + 2x = 90^@#

#3x=90^@#

#x=30^@#

so the angles are #60^@ and 30^@#

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Answer 2

Carson Arnold

Let's denote the measure of the angle as ( x ) degrees. Since the angle is twice as large as its complement, the complement angle can be represented as ( \frac{x}{2} ) degrees.

Since the sum of an angle and its complement is 90 degrees (as they form a right angle), we can write the equation:

[ x + \frac{x}{2} = 90 ]

To solve for ( x ), multiply both sides of the equation by 2 to eliminate the fraction:

[ 2x + x = 180 ] [ 3x = 180 ]

Divide both sides by 3:

[ x = \frac{180}{3} ] [ x = 60 ]

Therefore, the measure of the angle is 60 degrees, and its complement is ( \frac{60}{2} = 30 ) degrees.

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