Question

triangles abc and def are congruent, where a corresponds to d, and b and e are right angles. the measure of angle a is 18°. what is the measure of angle f?

Explanation:

Step1: Use congruent - angle property

Since \(\triangle ABC\cong\triangle DEF\) and \(A\) corresponds to \(D\), \(\angle A=\angle D = 18^{\circ}\).

Step2: Recall triangle - angle sum property

In \(\triangle DEF\), \(\angle E = 90^{\circ}\) (because \(B\) and \(E\) are right - angles), and the sum of interior angles of a triangle is \(180^{\circ}\). So \(\angle D+\angle E+\angle F=180^{\circ}\).

Step3: Solve for \(\angle F\)

Substitute \(\angle D = 18^{\circ}\) and \(\angle E = 90^{\circ}\) into the equation \(\angle D+\angle E+\angle F=180^{\circ}\). We get \(18^{\circ}+90^{\circ}+\angle F=180^{\circ}\), then \(\angle F=180^{\circ}-(18^{\circ} + 90^{\circ})=72^{\circ}\).

Answer:

\(72^{\circ}\)