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

Explanation:

Step1: Identify triangle type

Since $DE = DF = 3$, $\triangle DEF$ is an isosceles triangle. Let $\angle E=\angle F$. Also, $\angle D = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. In $\triangle DEF$, we have $\angle D+\angle E+\angle F = 180^{\circ}$. Substituting $\angle D = 90^{\circ}$ and $\angle E=\angle F$, we get $90^{\circ}+2\angle F=180^{\circ}$.

Step3: Solve for $\angle F$

First, subtract $90^{\circ}$ from both sides of the equation: $2\angle F=180^{\circ}- 90^{\circ}=90^{\circ}$. Then divide both sides by 2: $\angle F=\frac{90^{\circ}}{2}=45^{\circ}$.

Answer:

$45$