Question

What is the value of x? Enter your answer in the box.

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

TV/VY=TK/YK
77/22=87.5/YK
YK=1975/77
YK=25

VK=TK+YK
Vk=22+25
VK=47

So.VK(x)=47 feet

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Answer 2

• The value of x in the given figure is equal to 47 feet .

Given :-

• Y is on segment VK, between V and K .
• ∠VTY = ∠YTK
• VT = 77 feet
• VY = 22 feet
• TK = 87.5 feet

To Find :-

• VK = x = ?

Concept used :-

• Angle bisector theorem :- Angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides .

Solution :-

In ∆VTK we have given that,

→ ∠VTY = ∠YTK

So, we can conclude that, TY is angle bisector of ∠VTK .

then,

→ VT/TK = VY/YK { By angle bisector theorem }

putting given values we get,

→ 77/87.5 = 22/YK

→ 770/875 = 22/YK

→ 154/175 = 22/YK

→ 22/25 = 22/YK

→ YK = 25 feet

therefore,

→ VK = VY + YK

→ x = 22 + 25

→ x = 47 feet (Ans.)

Hence, the value of x is equal to 47 feet .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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