Question

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

Explanation:

Step1: Equate corresponding angles

Since $\triangle DEF\cong\triangle RST$, corresponding angles are equal. So, $6x - 8=4x + 8$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $6x-4x - 8=4x-4x + 8$, which simplifies to $2x-8 = 8$. Then add 8 to both sides: $2x-8 + 8=8 + 8$, giving $2x=16$. Divide both sides by 2: $x=\frac{16}{2}=8$.

Step3: Equate corresponding sides

Corresponding sides of congruent triangles are equal. So, $3y-12 = 51$.

Step4: Solve for $y$

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:

$x = 8$
$y = 21$