Question

in the diagram, triangle def ≅ triangle rst.
find the values of x and y.
enter your answers in the boxes.

Explanation:

Step1: Use congruent angles property

Since \(\triangle DEF\cong\triangle RST\), then \(\angle E=\angle S\). So, \(6x - 8=4x + 8\).
Subtract \(4x\) from both sides: \(6x-4x - 8=4x-4x + 8\), which gives \(2x-8 = 8\).
Add \(8\) to both sides: \(2x-8 + 8=8 + 8\), so \(2x=16\).
Divide both sides by \(2\): \(x=\frac{16}{2}=8\).

Step2: Use congruent sides property

Also, \(EF = ST\). But wait, no, since \(\triangle DEF\cong\triangle RST\), \(DE = RS\). So \(3y-12 = 51\).
Add \(12\) to both sides: \(3y-12 + 12=51 + 12\), which gives \(3y=63\).
Divide both sides by \(3\): \(y=\frac{63}{3}=21\).

Answer:

\(x = 8\)
\(y = 21\)