Complementary Angles have measures of 4x + 14, 3x - 22

J

Jeff24

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Mar 1, 2009
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If two complementary angles have measure of 4x + 14 and 3x -22 the smaller angle has what measure
So i would take
4x +14=3x-22
-14 -14
4x =3x-36
-3x -3x
x = -36

so x= -36
But how would i finen the smaller angle? Did is start to do the problem right?
 
Check the definition of "complementary" angles. In particular, what is the value of the sum of their measures? :wink:
 
Re: Complementary Angles?

two angles who have the sum of 90 degrees but how would i use that in this problem?
 


MY EDIT: This post was wrong, so I've deleted it. See my other post, below.

 
Re: Complementary Angles?

I got -12.5 for the first one.
But couldn't get -12.5 to work out for the second equation to = -36.
What's wrong?
 
Re: Complementary Angles?

never mind there not supposed to be the same!
 
Re: Complementary Angles?

For the first equation I have -12.5.
For the second equation I got can't get exactly -36.
When I can get 35.5 but I can't get exaclty -36.
 
WHOOPS!

I made a big mistake. (I think that I'm beginning to confuse your exercises.)

I previously told you that you started out right, but you didn't.

One angle is (4x + 14) degrees.

The other angle is (3x - 22) degrees.

These angles are complimentary, so their sum is 90 degrees.

Therefore, the equation is:

4x + 14 + 3x - 22 = 90

Solve THIS equation for x, instead.

Then, substitute the value that you get for x into the expression for each angle.

4x + 14 = ???

3x - 22 = ???

Compare these results to determine which one is smaller.

I apologize for my mistake, if I confused you.

 
Re: Complementary Angles?

It's fine,
This is what I did but I'm thinking x is to big!
4x+14=3x-22=90degres
-3x-14-3x-14
___________
x-36=90degrees
+36 +36
x=126 ( I think this number is WRONG!)
 
MathIQ said:
It's fine,
This is what I did but I'm thinking x is to big!
4x+14=3x-22=90degres
-3x-14-3x-14
___________
x-36=90degrees
+36 +36
x=126 ( I think this number is WRONG!)
Click to expand...


Your beginning equation contains two equals signs. I think that you meant to type the following, instead.

4x + 14 + 3x - 22 = 90

I'm not sure what you tried, after that.

The first step in solving this equation is to combine like terms on the left-hand side.

4x and 3x are like terms. They can be added to get 7x.

The constants 14 and -22 are like terms. They can be added to get -8.

After combining these like terms, we get a simplified equation.

7x - 8 = 90

Add 8 to both sides, to isolate the 7x term.

7x = 98

Now divide both sides by 7, to isolate x.

x = 98/7

(I leave the division of 98 by 7 for you to do.)

Substitute this value of x into the two given expressions.

4x + 14 = ???

3x - 22 = ???

Compare these results to see which angle is smaller.
 
Re: Complementary Angles?

so i got 70 and 20 as my final answer so 20 is the angle that has the smallest measure so I put that?
Just making sure.
 
I'm not sure why you think that "70 and 20" is your "final" answer.

There is only one answer to this exercise. Here it is:

"The smaller angle measures 20 degrees."

 
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