boothkelly996
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The supplement of the measurement of an angle is 16 degrees less than three times the angle. Find the measurement of the angle and its supplement.

Respuesta :

Let
x = measure of the angle
y = measure of the supplement 

By definition of supplementary, the two angles add to 180 degrees, so
x+y = 180
This is the first equation.

The second equation is y = 3x-16 since we're given the info that "the supplement is 16 degrees less than three times the angle"

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The system of equations is
x+y = 180
y = 3x-16

Focus on the first equation x+y = 180, plug in y = 3x-16, and solve for x

x+y = 180
x+3x-16 = 180  ... y is replaced with 3x-16
4x-16 = 180
4x-16+16 = 180+16
4x = 196
4x/4 = 196/4
x = 49

Because x = 49, we can use this to find y
y = 3x-16
y = 3*49-16
y = 147 - 16
y = 131

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Final Answers:
The measure of the angle is 49 degrees
The measure of the supplement is 131 degrees

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