Question

what value of X and Y makes CDE. = HFG

Answer 1

Congruent triangles have the same measure of their angles, this implies that

$\angle E=\angle G$

and they have exactly the same sides, this implies that

$DE=FG$

Since interior angles add up to 180 degrees, from triangle CDE, we get

$32+112+\angle E=180$

which gives

$\begin{gathered} 144+\angle E=180 \\ \angle E=180-144 \\ \angle E=36 \end{gathered}$

since angle G is equal to 4y+8, from our first relationship, we have

$36=4y+8$

then, by moving 8 to the left hand side, we have

$\begin{gathered} 36-8=4y \\ 28=4y \end{gathered}$

then y is given by

$\begin{gathered} y=\frac{28}{4} \\ y=7 \end{gathered}$

Now, by using our second relationship and the fact that DE=3x+2 and FG= 41, we have

$3x+2=41$

By moving 2 to the right hand side, wehave

$\begin{gathered} 3x=41-2 \\ 3x=39 \end{gathered}$

so, x is given by

$\begin{gathered} x=\frac{39}{3} \\ x=13 \end{gathered}$

Therefore, the answers are x=13 and y=7