Question

triangle abc is similar to triangle def. angle a measures 28°, and angle b measures 74°. if angle f is the largest angle in triangle def, what is the measure of angle f? type the answer in the box.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For \(\triangle ABC\), we know \(\angle A = 28^\circ\) and \(\angle B = 74^\circ\). First, find \(\angle C\) in \(\triangle ABC\).
\[
\angle C = 180^\circ - \angle A - \angle B = 180^\circ - 28^\circ - 74^\circ
\]

Step2: Calculate \(\angle C\)

\[
\angle C = 180 - 28 - 74 = 78^\circ
\]
Since \(\triangle ABC \sim \triangle DEF\), corresponding angles are equal. So \(\angle D = \angle A = 28^\circ\), \(\angle E = \angle B = 74^\circ\), and \(\angle F = \angle C\) (or the largest angle). Since \(78^\circ\) is larger than \(28^\circ\) and \(74^\circ\), \(\angle F = 78^\circ\).

Answer:

\(78\)