Question

What is the value of x? Enter your answer in the box. Ft Triangle V T K with segment T Y such that Y is on segment V K, between V and K. Angle V T Y is congruent to angle Y T K. V T equals 77 feet, V Y equals 22 feet, V K equals x, and T K equals 87.5 feet.

Answer 1

Answer:

x=47 feet

Step-by-step explanation:

Since angle VTY is congruent to angle VTK, segment TY bisects angle VTK. Since Y is on segment VK, between V and K, we can use the Angle Bisector Theorem, which states that:

$\frac{VY}{YK}=\frac{VT}{TK}$

$\frac{22}{YK}=\frac{77}{87.5}$

$YK=\frac{22{\times}87.5}{77}$

$YK=25 feet$

Now, X=VY+YK

Substituting the values, we get

X=$22+25$

X=$47 feet$

Answer 2

Answer:

47 ft

Step-by-step explanation: