Question

△abc ≅ △def
determine the following measures. enter deg after any value that is in
degrees.
the length of ac.

the measure of m\angle f.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), corresponding sides and angles are equal.
For side \(AC\), its corresponding side is \(DF\). So \(AC = DF\).

Step2: Find the measure of \(\angle F\)

In \(\triangle ABC\), \(\angle A = 44^{\circ}\), \(\angle E=48^{\circ}\) (in \(\triangle DEF\)).
We know that the sum of angles in a triangle is \(180^{\circ}\).
In \(\triangle ABC\) (or \(\triangle DEF\) as they are congruent), \(\angle A+\angle B+\angle C=\angle D+\angle E+\angle F = 180^{\circ}\).
Since \(\angle A=\angle D = 44^{\circ}\), \(\angle E=\angle B = 48^{\circ}\).
Then \(\angle F=\angle C\).
\(\angle F=180^{\circ}-\angle D-\angle E\)
\(\angle F = 180^{\circ}-44^{\circ}-48^{\circ}\)

Answer:

\(AC = 10.7\) m
\(m\angle F=88\) deg