Confused by Geometry Problem - Can You Help?

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    Confused Geometry
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The geometry problem involves finding the measure of angle S, which is stated to be 20 more than four times its supplement. The initial setup incorrectly defines the supplement and leads to a miscalculation. The correct approach requires recognizing that the supplement of angle S is 180 - x, not x - 180. The user realizes their mistake in the calculation and seeks clarification on the proper method to solve the problem. Understanding the definitions and relationships between angles is crucial for arriving at the correct answer.
Imparcticle
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I was doing my geometry homework earlier and came across a problem:

Find m<S if m<S is 20 more than four times its supplement.

What I did:
m<S= x
supplement of m<S: x = (x-180)

how I worked it out:
x=4(x-180) + 20
x=4x-700
700=3x
233.333... = x

My answer for x is obviously wrong because when I try to find m<S, I get 233.33... again:
x=4(2.333...-180) +20
4(53.33...)= 213.333... + 20 = 233.3333...

This evidently does not make any sense at all. The problem said "supplement", and 233.333... is most certainly not an angle measure which agree with the definition of supplement, I believe.

Please help.
 
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180-x .
 
okay. That does not make a difference.
 
yes .
 
Imparcticle said:
okay. That does not make a difference.

my mistake. It does make a difference.
 

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