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natta225 [31]
3 years ago
5

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

nd its supplement.
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
3 0
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"

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

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

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

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

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Answer:

m∠1 = 60°

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Step-by-step explanation:

ΔWXY is a equilateral angle,

Therefore, all angles of the the triangle are equal in measure.

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3m∠W = 180°

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Since, ΔWZY is an isosceles triangle,

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m∠3 + m∠Z + m∠5 = 180°

m∠3 + 138° + m∠3 = 180°

2m∠3 = 180 - 138

m∠3 = 21°

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m∠2 = 60 - 21

        = 39°

Since, m∠4 + m∠5 = 60°

m∠4 = 60 - 21

        = 39°

m∠1 = 60°

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