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? a 18° b 72° c 90° d 162°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle \(ABC\), \(\angle A+\angle B+\angle C = 180^{\circ}\). Given \(\angle A = 18^{\circ}\) and \(\angle B=90^{\circ}\).

Step2: Calculate \(\angle C\)

\(\angle C=180^{\circ}-\angle A - \angle B=180^{\circ}-18^{\circ}-90^{\circ}=72^{\circ}\).

Step3: Use congruence property

Since \(\triangle ABC\cong\triangle DEF\) and \(\angle C\) corresponds to \(\angle F\) (by the congruence of the triangles where \(A\) corresponds to \(D\) and \(B\) corresponds to \(E\)), \(\angle F=\angle C\).

Answer:

B. \(72^{\circ}\)