Question

1. in the figure, \\(\overrightarrow{yw}\\) bisects \\(\angle xwz\\). fill in the following blanks. (lesson 8.2) (2 points)

a. \\(m\angle xwy = m\angle \underline{\qquad}\\)

b. if \\(xy = 9\text{ cm}\\), then \\(zy = \underline{\qquad}\\)

c. solve for \\(x\\). once you solve for \\(x\\), take a look at the four student solutions below. only one of the student solutions shown below is correct. circle the student whose work is correct.

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$$\begin{array}{|l|l|l|l|} \\hline \\textbf{joshs solution:} & \\textbf{alys solution:} & \\textbf{karis solution:} & \\textbf{vivians solution:} \\\\ 7x - 20 - 2x - 5 = 180 & 7x - 20 = 2x - 5 & 7x - 20 + 2x - 5 = 90 & 7x - 20 = 2x - 5 \\\\ 5x - 25 = 180 & 5x - 20 = -5 & 9x - 25 = 90 & 9x = -25 \\\\ 5x = 205 & 5x = 15 & 9x = 115 & x = -\\frac{25}{9} \\\\ x = \\frac{205}{5} & x = \\frac{15}{5} & x = \\frac{115}{9} & x = 2.78 \\\\ x = 41 & x = 3 & x = 12.78 & \\\\ \\hline \\end{array}$$

Explanation:

Identify bisected angles and segment lengths

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Set up and solve the equation for x

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Identify the correct student solution

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Answer:

Question 1

a. \(m\angle XWY = m\angle\) <blank>\(ZWY\)</blank>

Question 2

b. If \(XY = 9\text{ cm}\), then \(ZY =\) <blank>\(9\text{ cm}\)</blank>

Question 3

c. Solve for \(x\). Once you solve for \(x\), take a look at the four student solutions below. Only one of the student solutions shown below is correct. Circle the student whose work is correct.
The student whose work is correct is <blank>Aly</blank>.