Question
In the diagram shown below, s∥t
and r
is a transversal.
GEO T3-4 GR.1.1.png
Part A: Nia performed the calculations below to find the value of x
. Click on the step where Nia made a mistake.
Step 1 (7x−20) + (4x+16) = 180
Step 2 11x−4=180
Step 3 11x=184
Step 4 16.7
Part B: What is the correct value of x
?
16.7
12
10
8.5
and r
is a transversal.
GEO T3-4 GR.1.1.png
Part A: Nia performed the calculations below to find the value of x
. Click on the step where Nia made a mistake.
Step 1 (7x−20) + (4x+16) = 180
Step 2 11x−4=180
Step 3 11x=184
Step 4 16.7
Part B: What is the correct value of x
?
16.7
12
10
8.5
Answers
GPT-4o mini
To evaluate Nia's calculations step-by-step and identify the mistake in her reasoning, we need to analyze each step.
### Part A: Identifying the mistake
1. **Step 1**: \( (7x - 20) + (4x + 16) = 180 \)
- This step represents the sum of two angles that are supplementary since the lines \( s \) and \( t \) are parallel and \( r \) is a transversal. This step is correct.
2. **Step 2**: \( 11x - 4 = 180 \)
- Here, Nia combines \( 7x \) and \( 4x \), which correctly gives \( 11x \), but she also combines \( -20 \) and \( +16 \). The correct result should be \( -20 + 16 = -4 \); therefore, this step is also correct.
3. **Step 3**: \( 11x = 184 \)
- Here, this appears to be where she made her mistake. She should have added \( 4 \) to both sides of the equation in Step 2 to obtain:
\[
11x - 4 + 4 = 180 + 4
\]
This means she should have had:
\[
11x = 184
\]
Nia’s mistake is not caused by the arithmetic in Step 2, but rather a misunderstanding of the operation on Step 3.
4. **Step 4**: \( x = 16.7 \)
- This step is incorrect if she calculated \( 11x = 184 \) correctly, then \( x \) would equal:
\[
x = \frac{184}{11} \approx 16.73,
\]
Hence 16.7 is approximately correct but she is nearer if a decimal answer is nearing.
### Part B: Correct value of x
To correctly find \( x \), we should continue from Step 3:
Starting from \( 11x = 184 \):
\[
x = \frac{184}{11} \approx 16.73.
\]
However, the original question offers options, and we need the closest valid answer:
The values given are:
- 16.7
- 12
- 10
- 8.5
The correct value of \( x \) based on calculations being approximately 16.7, is:
**Answer: 16.7**.
### Part A: Identifying the mistake
1. **Step 1**: \( (7x - 20) + (4x + 16) = 180 \)
- This step represents the sum of two angles that are supplementary since the lines \( s \) and \( t \) are parallel and \( r \) is a transversal. This step is correct.
2. **Step 2**: \( 11x - 4 = 180 \)
- Here, Nia combines \( 7x \) and \( 4x \), which correctly gives \( 11x \), but she also combines \( -20 \) and \( +16 \). The correct result should be \( -20 + 16 = -4 \); therefore, this step is also correct.
3. **Step 3**: \( 11x = 184 \)
- Here, this appears to be where she made her mistake. She should have added \( 4 \) to both sides of the equation in Step 2 to obtain:
\[
11x - 4 + 4 = 180 + 4
\]
This means she should have had:
\[
11x = 184
\]
Nia’s mistake is not caused by the arithmetic in Step 2, but rather a misunderstanding of the operation on Step 3.
4. **Step 4**: \( x = 16.7 \)
- This step is incorrect if she calculated \( 11x = 184 \) correctly, then \( x \) would equal:
\[
x = \frac{184}{11} \approx 16.73,
\]
Hence 16.7 is approximately correct but she is nearer if a decimal answer is nearing.
### Part B: Correct value of x
To correctly find \( x \), we should continue from Step 3:
Starting from \( 11x = 184 \):
\[
x = \frac{184}{11} \approx 16.73.
\]
However, the original question offers options, and we need the closest valid answer:
The values given are:
- 16.7
- 12
- 10
- 8.5
The correct value of \( x \) based on calculations being approximately 16.7, is:
**Answer: 16.7**.