In the diagram shown below, s∥t

Question

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

Answer 1

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.