Complementary and supplementary angles and finding measures

H

hansbar

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Sep 19, 2006
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"The supplement of an angle if four times the complement of the angle. Find the measure of the complement."

So far, what I have done is
c= complementary
s= supplementary


c=4(180-s)
c= 720-4s

I'm not sure if I even started the question right.
I know I need another equation, but I'm not sure how to find it.

I know the answer is 30, I just dont know to arrive at that point.
 
\(\displaystyle \L
\left( {180 - \phi } \right) = 4\left( {90 - \phi } \right).\)
 
You have three unknowns, two of which you've labelled. But those two can be expressed in terms of the third.

Pick a variable for the measure of the angle; say, "a".

By definition, what then is the expression, in terms of "a", for the complement of "a"?

By definition, what is the expression for the supplement of "a"?

You know that the supplement is (equals) four times the complement. Translate the preceeding sentence into an equation, and solve for "a". Back-solve for the value of the complement.

Eliz.
 
stapel said:
You have three unknowns, two of which you've labelled. But those two can be expressed in terms of the third.

Pick a variable for the measure of the angle; say, "a".

By definition, what then is the expression, in terms of "a", for the complement of "a"?

By definition, what is the expression for the supplement of "a"?

You know that the supplement is (equals) four times the complement. Translate the preceeding sentence into an equation, and solve for "a". Back-solve for the value of the complement.

Eliz.
Click to expand...
I wrote down
measure of angle=A
A+C=90
A+S=180

I'm still so confused, I have no idea what to do

[by the way, thank you so so so so so much for your help.]

The answer IS 30. That was the only help my teacher would give me
 
If you solve the equation I posted above and find the complement of \(\displaystyle \phi\) it will work.
 
pka said:
If you solve the equation I posted above and find the complement of \(\displaystyle \phi\) it will work.
Click to expand...
I'm sorry... does \phi represent the measure of the angle?
 
Just solve for \(\displaystyle \phi\). See what you get.
 
pka said:
Just solve for \(\displaystyle \phi\). See what you get.
Click to expand...

I get 60.

[I exchanged your symbol for A]
180-a= 4(90-A)
180-A=360-4A
+4A +4A

180+3A=360
-180 -180
3A=180
/3 /3
a=60
 
The question asks for the complement. RIGHT?
The complement of 60 is 30.
 
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