find the largest angle of $\triangle efg$. assume that $x$ is a positive number.

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Accepted Answer

# Explanation:
## Step1: Recall the triangle side-angle relationship
In a triangle, the largest angle is opposite the longest side. So we first need to determine the longest side of $\triangle EFG$.

The side lengths are $33x$ (opposite $\angle F$), $48x$ (opposite $\angle G$), and $51x$ (opposite $\angle E$). Since $x>0$, we can compare the coefficients: $51>48>33$, so $51x$ is the longest side.

## Step2: Identify the angle opposite the longest side
The side $51x$ is $FG$, and the angle opposite $FG$ is $\angle E$ (because in $\triangle EFG$, side $FG$ is between $F$ and $G$, so the angle opposite is at $E$). By the side - angle relationship (larger side opposite larger angle), the angle opposite the longest side ($51x$) is the largest angle.

# Answer:
The largest angle of $\triangle EFG$ is $\angle E$ (the angle opposite the side of length $51x$).

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Question

Explanation:

Step1: Recall the triangle side-angle relationship

Step2: Identify the angle opposite the longest side

Answer: