finding the measure of angles

[rachelmaddie]

Is this correct?
48+ 8x - 3 + 180 - (18x + 5) = 180

 

[lev888]

Is this correct?
48+ 8x - 3 + 180 - (18x + 5) = 180View attachment 14783

Looks good.

 

[Romsek]

For clarity I would have written it as

48 + (8x-3) + (180-(18x+5)) = 180

but what you have is correct.

 

[rachelmaddie]

For clarity I would have written it as

48 + (8x-3) + (180-(18x+5)) = 180

but what you have is correct.

I’m having trouble combining the like terms and numeric values.

 

[Romsek]

persevere.

by inspection you can see that WZX is a bit less than 90 deg

(though it's fair to say that one has to treat pictures with caution)

continue methodically until you reach an answer that fits this

 

[rachelmaddie]

persevere.

by inspection you can see that WZX is a bit less than 90 deg

(though it's fair to say that one has to treat pictures with caution)

continue methodically until you reach an answer that fits this

48 + (5x) + (180 - (23x)) = 180

 

[Romsek]

how about writing it like

48 + 180 + 5x -23x = 180

does that help you combine the like terms any?

 

[rachelmaddie]

48 + 180 + 5x -23x = 180

132 + 5x -23x = 180

132 + (-18x) = 180

This is what I keep getting.

 

[HallsofIvy]

48 + (8x-3) + (180-(18x+5)) = 180

The "like terms" are 8x- 18x and 48- 3+ 180- 5.

 

[pka]

Is this correct?
48+ 8x - 3 + 180 - (18x + 5) = 180View attachment 14783

This question is testing your knowledge of the external angle theorem.
\(\displaystyle \angle XZW\) is an external angle of triangle \(\displaystyle \Delta XZY\).
The theorem: The measure of an external angle is equal to the sum of the measures of the opposite two interior angles.
Applying that theorem we get \(\displaystyle 18x+5=(48)+(8x-3)\).

 

[Deleted member 4993]

48 + 180 + 5x -23x = 180

132 + 5x -23x = 180

132 + (-18x) = 180

This is what I keep getting.

Now isolate "x" terms. To do so, you need to have 'only x terms' on one side. Here that can be accomplished by subtracting 132 from both sides:

132 + (-18x) = 180

132 + (-18x) -132 = 180 - 132

Continue......

 

[rachelmaddie]

48 + (8x-3) + (180-(18x+5)) = 180

The "like terms" are 8x- 18x and 48- 3+ 180- 5.

Was that correct my work? I need help with solving for x.

 

[rachelmaddie]

Was that correct my work? I need help with solving for x.

Im getting confused because different ways are being shown and not the step process.

 

[rachelmaddie]

48 + (8x-3) + (180-(18x+5)) = 180

The "like terms" are 8x- 18x and 48- 3+ 180- 5.

46 + (-10x) + 175 = 180
129 + (-10x) = 180
(-10x) = 51
x = -5.1

 

[lev888]

Im getting confused because different ways are being shown and not the step process.

You seemed to be comfortable with equations like this before.
Step 1: combine terms with x on the left, without x on the right
Step 2: find x.

 

[rachelmaddie]

This question is testing your knowledge of the external angle theorem.
\(\displaystyle \angle XZW\) is an external angle of triangle \(\displaystyle \Delta XZY\).
The theorem: The measure of an external angle is equal to the sum of the measures of the opposite two interior angles.
Applying that theorem we get \(\displaystyle 18x+5=(48)+(8x-3)\).

18x + 5 = (48) + (8x -3)
10x = 50
x = 5

 

[JeffM]

46 + (-10x) + 175 = 180
129 + (-10x) = 180
(-10x) = 51
x = -5.1

Where did 46 come from?

[MATH]48 + (8x - 3) +\{180 - (18x + 5)\} = 180 \implies[/MATH]
[MATH]48 - 3 + 8x + 180 - 5 - 18x = 180 \implies[/MATH]
[MATH]45 + 175 + 8x - 18x = 180 \implies[/MATH]
[MATH]220 - 10x = 180 \implies[/MATH]
[MATH]220 - 180 = 10x \implies[/MATH]
[MATH]10x = 40 \implies[/MATH]
[MATH]x = 4 \implies[/MATH]
[MATH]18x + 5 = 18 * 4 + 5 = 72 + 5 = 79.[/MATH]
Now check your work.

[MATH]48 + (8 * 4 - 3) + 103 = 48 + 32 - 3 + 103 = 80 + 100 = 180.[/MATH] OK

[MATH]103 + (18 * 4 + 5) = 108 + 72 = 180.[/MATH] OK

 

[JeffM]

18x + 5 = (48) + (8x -3)
10x = 50
x = 5

Always check your work

[MATH]18 * 5 + 5 = 90 + 5 = 95.[/MATH]
[MATH]48 + (8 * 5 - 3) = 48 + 40 - 3 = 88 - 3 = 85.[/MATH]
Does 85 = 95.

[MATH]18x + 5 = 48 + 8x - 3 = 45 + 8x \implies[/MATH]
[MATH]18x - 8x = 45 - 5 = 40 \implies[/MATH]
[MATH]10x = 40 \implies[/MATH]
[MATH]x = 4.[/MATH]
Which does check.

But you are forgetting that the problem does not even ask you to find x. It asks you to find 18x + 5.

 

[rachelmaddie]

Where did 46 come from?

[MATH]48 + (8x - 3) +\{180 - (18x + 5)\} = 180 \implies[/MATH]
[MATH]48 - 3 + 8x + 180 - 5 - 18x = 180 \implies[/MATH]
[MATH]45 + 175 + 8x - 18x = 180 \implies[/MATH]
[MATH]220 - 10x = 180 \implies[/MATH]
[MATH]220 - 180 = 10x \implies[/MATH]
[MATH]10x = 40 \implies[/MATH]
[MATH]x = 4 \implies[/MATH]
[MATH]18x + 5 = 18 * 4 + 5 = 72 + 5 = 79.[/MATH]
Now check your work.

[MATH]48 + (8 * 4 - 3) + 103 = 48 + 32 - 3 + 103 = 80 + 100 = 180.[/MATH] OK

[MATH]103 + (18 * 4 + 5) = 108 + 72 = 180.[/MATH] OK

what does the y variable represent?

 

[rachelmaddie]

Where did 46 come from?

[MATH]48 + (8x - 3) +\{180 - (18x + 5)\} = 180 \implies[/MATH]
[MATH]48 - 3 + 8x + 180 - 5 - 18x = 180 \implies[/MATH]
[MATH]45 + 175 + 8x - 18x = 180 \implies[/MATH]
[MATH]220 - 10x = 180 \implies[/MATH]
[MATH]220 - 180 = 10x \implies[/MATH]
[MATH]10x = 40 \implies[/MATH]
[MATH]x = 4 \implies[/MATH]
[MATH]18x + 5 = 18 * 4 + 5 = 72 + 5 = 79.[/MATH]
Now check your work.

[MATH]48 + (8 * 4 - 3) + 103 = 48 + 32 - 3 + 103 = 80 + 100 = 180.[/MATH] OK

[MATH]103 + (18 * 4 + 5) = 108 + 72 = 180.[/MATH] OK

The check my work part is confusing me.