Question

△fgh is rotated 180° and translated down to form △fgh. what is the measure of ∠f? m∠f = (square^{circ})

Explanation:

Step1: Recall transformation properties

Rotations and translations are rigid - motions. Rigid - motions preserve angle measures.

Step2: Identify corresponding angles

Since $\triangle FGH$ is transformed to $\triangle F'G'H'$ by rotation and translation, $\angle F$ corresponds to $\angle F'$, $\angle G$ corresponds to $\angle G'$, and $\angle H$ corresponds to $\angle H'$.

Step3: Use angle - sum property of a triangle

In $\triangle F'G'H'$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle F' = x$, $m\angle G'=22^{\circ}$, and $m\angle H' = 118^{\circ}$. Then $x + 22^{\circ}+118^{\circ}=180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}-(22^{\circ} + 118^{\circ})$.
$x = 40^{\circ}$. Since $m\angle F=m\angle F'$, $m\angle F = 40^{\circ}$.

Answer:

$40$