Question

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if vw = t + 77 and xz = 6t, what is the value of t?
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t = \boxed{}

Explanation:

Step1: Identify Midsegment Property

In a triangle, the midsegment (segment connecting midpoints of two sides) is parallel to the third side and half its length. Here, \( Z \) and \( X \) are midpoints (marked by congruent segments), so \( XZ \) is the midsegment, meaning \( XZ=\frac{1}{2}VW \).

Step2: Set Up Equation

Substitute \( VW = t + 77 \) and \( XZ = 6t \) into the midsegment formula: \( 6t=\frac{1}{2}(t + 77) \).

Step3: Solve for \( t \)

Multiply both sides by 2: \( 12t=t + 77 \).
Subtract \( t \) from both sides: \( 11t = 77 \).
Divide by 11: \( t = 7 \).

Answer:

\( 7 \)