Question

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

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), corresponding sides are equal. So \(AC = DF\). Given \(DF = 10m\), so \(AC=10m\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle DEF\), \(\angle D+\angle E+\angle F = 180^{\circ}\). Since \(\triangle ABC\cong\triangle DEF\), \(\angle A=\angle D = 63^{\circ}\), \(\angle E = 58^{\circ}\).
Substitute into the angle - sum formula: \(63^{\circ}+58^{\circ}+\angle F=180^{\circ}\).
First, add \(63^{\circ}\) and \(58^{\circ}\): \(63 + 58=121\). Then \(\angle F=180 - 121\).
\(\angle F = 59^{\circ}\)

Answer:

\(AC = 10m\)
\(m\angle F=59deg\)