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Answer the following questions about the figure below: (a) What is the value of “x”? (b) What is the value of “y”? (c) What is the value of “z”? (d) What is the value of “t”?

Answer the following questions about the figure below: (a) What is the value of “x-example-1
User YU FENG
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1 Answer

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Given that ΔJKL is similar to ΔDEF.

To find the side lengths, we have:


(DF)/(JL)=(DE)/(JK)=(EF)/(KL)

Let's solve for y:


\begin{gathered} (13)/(y+8)=(10)/(8) \\ \\ \text{Cross multiply:} \\ 10(y+8)=8(13) \\ \\ 10y+80=104 \\ \\ 10y+80-80=104-80 \\ \\ 10y=24 \end{gathered}

Divide both sides by 10:


\begin{gathered} (10y)/(10)=(24)/(10) \\ \\ y=2.4 \end{gathered}

Let's solve for x:


\begin{gathered} (x-7)/(12)=(10)/(8) \\ \\ 8(x-7)=10(12) \\ \\ 8x-56=120 \\ \\ 8x-56+56=120+56 \\ \\ 8x=176 \\ \\ (8x)/(8)=(176)/(8) \\ \\ x=22 \end{gathered}

Since they are similar triangles the corresponding angles are congruent.

Thus, we have:

z = 77 degrees

To solve for t, use the triangle angle sum theorem, which states that the sum of interior angles in a triangle is 180 degrees.

Therefore, we have:

t + 77 + 43 = 180

t + 120 = 180

Subtract 120 from both sides:

t + 120 - 120 = 180 - 120

t = 60 degrees

ANSWER:

a) x = 22

b) y = 2.4

c) z = 77°

d) t = 60°

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