Question

question
in the diagram below of triangle vwx, y is the midpoint of \\(\overline{vx}\\) and z is the midpoint of \\(\overline{wx}\\). if m\\(\angle xwv = 43 - 2x\\), and m\\(\angle xzy = -9x + 85\\), what is the measure of \\(\angle xzy\\)?
answer attempt 1 out of 2
m\\(\angle xzy = \square\\) \\(^\circ\\)
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Explanation:

Step1: Identify the relationship

Since \( Y \) is the midpoint of \( \overline{VX} \) and \( Z \) is the midpoint of \( \overline{WX} \), by the Midline Theorem (also known as the Midsegment Theorem), \( YZ \parallel VW \). Therefore, \( \angle XWV \) and \( \angle XZY \) are corresponding angles, so they are equal. So we set up the equation:
\( 43 - 2x = -9x + 85 \)

Step2: Solve for \( x \)

Add \( 9x \) to both sides:
\( 43 - 2x + 9x = 85 \)
Simplify:
\( 43 + 7x = 85 \)
Subtract 43 from both sides:
\( 7x = 85 - 43 \)
\( 7x = 42 \)
Divide both sides by 7:
\( x = \frac{42}{7} = 6 \)

Step3: Find \( m\angle XZY \)

Substitute \( x = 6 \) into the expression for \( m\angle XZY \):
\( m\angle XZY = -9x + 85 \)
\( m\angle XZY = -9(6) + 85 \)
\( m\angle XZY = -54 + 85 \)
\( m\angle XZY = 31 \)

Answer:

\( 31 \)