Question

△fgh is rotated 180° and translated down to form △fgh.
what is the measure of ∠f?
m∠f = °

Explanation:

Step1: Use the property of rotation and translation

Rotation and translation are rigid transformations. Rigid transformations preserve the shape and size of the figure. So, \(\triangle FGH\cong\triangle F'G'H'\). Corresponding angles of congruent triangles are equal.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle FGH\), if we let \(m\angle F = x\), \(m\angle G=22^{\circ}\), \(m\angle H = 118^{\circ}\). Then \(x + 22^{\circ}+118^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(40\)