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What value of X and Y makes CDE. = HFG

What value of X and Y makes CDE. = HFG-example-1
User Hotfix
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1 Answer

23 votes
23 votes

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=(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=(39)/(3) \\ x=13 \end{gathered}

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

User Eat
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