find m∠e. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠e = °

Explanation:

Step1: Recall tangent - ratio formula

In right - triangle $FGE$, $\tan E=\frac{opposite}{adjacent}=\frac{FG}{GE}$. Here, $FG$ is the side opposite to $\angle E$ and $GE$ is the side adjacent to $\angle E$. Given $FG = 3$ and $GE = 7$.

Step2: Calculate the tangent of $\angle E$

$\tan E=\frac{3}{7}\approx0.4286$.

Step3: Find the measure of $\angle E$

We know that if $\tan E = x$, then $E=\arctan(x)$. So, $E=\arctan(0.4286)$. Using a calculator in degree mode, $E\approx23.2^{\circ}$.

Answer:

$23.2$