Question

1. triangles abc and def are similar.

find the measure of the missing angle.
m∠f = degrees

Explanation:

Step1: Recall similar triangles property

Similar triangles have corresponding angles equal. Also, the sum of angles in a triangle is \(180^\circ\). For \(\triangle DEF\), we know two angles: \(\angle D = 41^\circ\) and \(\angle E = 78^\circ\).

Step2: Calculate \(\angle F\)

Using the angle - sum property of a triangle (\(m\angle D + m\angle E+m\angle F=180^\circ\)), we substitute the known values:
\(41^\circ+78^\circ + m\angle F=180^\circ\)
First, calculate \(41 + 78=119\). Then, \(m\angle F=180^\circ - 119^\circ\)
\(m\angle F = 61^\circ\)

Answer:

\(61\)