4 times the measure of the complement of an angle is equal to / the measure of the original angle's supplement. What is the measure of the angle?

18°
48°
72°
108°

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John5188 John5188 · Answer 1 · 2017-03-27T18:25:05+02:00

The measure of the angle is 18 degrees because 18 x 4 = 72 degrees

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akposevictor akposevictor · Answer 2 · 2022-06-22T11:30:34+02:00

Applying the definition of complement and supplement of an angle, the measure of the angle is calculated as: C. C. 72°.

The complement of an angle is the angle measure that will sum up to the angle to give 90 degrees.

Angles that add up to 180 degrees are supplementary angles.

Let x represent the angle.

Complement of x is: 90 - x

Supplement of x is: 180 - x

Therefore, we would have the following equation

4(90 - x) = 2/3(180 - x)

360 - 4x = (360 - 2x)/3

3(360 - 4x) = 360 - 2x

1080 - 12x = 360 - 2x

1080 - 360 = 12x - 2x

720 = 10x

720/10 = x

72 = x

x = 72°

The measure of the angle is: C. 72°

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