Question

select the correct answer. the triangles in the diagram are congruent. if m∠f = 40°, m∠a = 80°, and m∠g = 60°, what is m∠b?

Explanation:

Step1: Recall triangle congruence and angle sum

Since triangles are congruent, corresponding angles are equal. Also, triangle angle sum is \(180^\circ\).

Step2: Identify corresponding angles

In congruent triangles, \(\angle A\) corresponds to \(\angle E\), \(\angle C\) corresponds to \(\angle G\), and \(\angle B\) corresponds to \(\angle F\)? Wait, no, wait. Wait, let's check the congruence. Wait, the triangles are \(\triangle ABC\) and \(\triangle EFG\) (assuming). Wait, given \(m\angle F = 40^\circ\), \(m\angle A = 80^\circ\), \(m\angle G = 60^\circ\). Wait, in a triangle, sum of angles is \(180^\circ\). Wait, maybe \(\triangle ABC \cong \triangle EFG\), so \(\angle B\) corresponds to \(\angle F\)? No, wait, maybe I mixed up. Wait, let's calculate the angle in \(\triangle EFG\): sum of angles is \(180^\circ\), so \(m\angle E + m\angle F + m\angle G = 180^\circ\). Wait, but \(\triangle ABC\) and \(\triangle EFG\) are congruent, so corresponding angles are equal. Wait, maybe \(\angle A\) corresponds to \(\angle E\), \(\angle B\) corresponds to \(\angle F\), \(\angle C\) corresponds to \(\angle G\)? Wait, no, let's re - evaluate. Wait, the problem says "the triangles in the diagram are congruent". Let's use the angle - sum property. In any triangle, the sum of interior angles is \(180^\circ\). Also, since the triangles are congruent, their corresponding angles are equal. Wait, maybe \(\angle B\) corresponds to \(\angle F\)? No, wait, let's check the given angles. Wait, \(m\angle F = 40^\circ\), \(m\angle A = 80^\circ\), \(m\angle G = 60^\circ\). Let's find the angle in \(\triangle EFG\): \(m\angle E=180 - 40 - 60=80^\circ\). Now, since the triangles are congruent, \(\angle A=\angle E = 80^\circ\), \(\angle C=\angle G = 60^\circ\), so \(\angle B=\angle F = 40^\circ\)? Wait, no, wait, maybe I got the correspondence wrong. Wait, another way: in \(\triangle ABC\), sum of angles is \(180^\circ\), so \(m\angle A + m\angle B + m\angle C=180^\circ\). In \(\triangle EFG\), \(m\angle E + m\angle F + m\angle G = 180^\circ\). Since they are congruent, \(m\angle A=m\angle E\), \(m\angle B=m\angle F\), \(m\angle C=m\angle G\) (or other correspondence, but let's check the values). Given \(m\angle F = 40^\circ\), \(m\angle A = 80^\circ\), \(m\angle G = 60^\circ\). Let's assume that \(\angle B\) corresponds to \(\angle F\), then \(m\angle B=m\angle F = 40^\circ\)? Wait, no, wait, maybe the correspondence is \(\angle A\) with \(\angle E\), \(\angle B\) with \(\angle F\), \(\angle C\) with \(\angle G\). Wait, \(m\angle A = 80^\circ\), so \(m\angle E = 80^\circ\), \(m\angle G = 60^\circ\), so \(m\angle C = 60^\circ\), then in \(\triangle ABC\), \(m\angle B=180-(80 + 60)=40^\circ\), which is equal to \(m\angle F\). So \(m\angle B = 40^\circ\).

Answer:

\(40^\circ\)