Question

let ( \triangle abccong\triangle def ). find ( mangle f ).
( mangle f=square^{circ} )
(simplify your answer.)

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle ABC\), \(m\angle A + m\angle B + m\angle C=180^{\circ}\). Given \(m\angle A = 34^{\circ}\), \(m\angle B=115^{\circ}\). Then \(m\angle C=180-(34 + 115)=180 - 149 = 31^{\circ}\).

Step2: Use congruent triangle property

Since \(\triangle ABC\cong\triangle DEF\), corresponding angles are equal. \(\angle C\) corresponds to \(\angle F\). So \(m\angle F=m\angle C\).

Answer:

\(31\)