73.9k views
5 votes
What is the value of x? 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 57 millimeters, V K equals x, Y K equals 68 millimeters, and T K equals 129.2 millimeters.

2 Answers

5 votes

Answer:

98

Step-by-step explanation:

Confirming that this answer is correct! :)

User JhonnyTawk
by
8.2k points
1 vote
Answer: 98 millimeters

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


(VY)/(YK) = (VT)/(TK) (1)

Since x= VK = VY + YK, we need to obtain VY since YK = 68.

VY is obtained by multiplying the denominator YK on both sides of equation (1). So,


VY = ((VY)(VT))/(TK) = ((68)(57))/(129.2) \\ewline VY = 30

Hence,

x = VK = VY + YK
x = 30 + 68
x = 98 millimeters
User Imon
by
6.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories