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question
in the diagram below of triangle uvw, x is the midpoint of (overline{uw}) and y is the midpoint of (overline{vw}). if m(angle wvu = 20 + 4x), and m(angle wyx = 8x - 16), what is the measure of (angle wvu)?
answer attempt 1 out of 2
m(angle wvu =) (square) (degree)
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Explanation:

Step1: Identify the relationship (Midline Theorem)

Since \( X \) is the midpoint of \( \overline{UW} \) and \( Y \) is the midpoint of \( \overline{WV} \), by the Midline Theorem, \( XY \parallel UV \). Therefore, \( \angle WVU \) and \( \angle WYX \) are corresponding angles, so they are equal. Thus, we set up the equation:
\( 20 + 4x = 8x - 16 \)

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 20 = 4x - 16 \)

Add 16 to both sides:
\( 36 = 4x \)

Divide both sides by 4:
\( x = 9 \)

Step3: Find \( m\angle WVU \)

Substitute \( x = 9 \) into \( m\angle WVU = 20 + 4x \):
\( m\angle WVU = 20 + 4(9) = 20 + 36 = 56 \)

Answer:

\( 56 \)