Question

the triangles in the diagram are congruent. if ( mangle f = 40^{circ}), ( mangle a = 80^{circ}), and ( mangle g = 60^{circ}), what is ( mangle b)?

a. ( 40^{circ})
b. ( 60^{circ})
c. ( 80^{circ})
d. ( 100^{circ})

Explanation:

Step1: Use congruent triangles property

Since the triangles are congruent, corresponding angles are equal.

Step2: Recall triangle angle - sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). For \(\triangle ABC\) and \(\triangle FEG\) (assuming congruence), \(\angle A\) corresponds to \(\angle F\) (no, wait, actually, from the side - marking (equal sides), \(\triangle ABC\cong\triangle EFG\). So \(\angle A\) in \(\triangle ABC\) and \(\angle E\) in \(\triangle EFG\) are not the key. Wait, using the fact that in \(\triangle EFG\), \(m\angle F = 40^{\circ}\), \(m\angle G=60^{\circ}\). In \(\triangle ABC\), \(m\angle A = 80^{\circ}\). But by congruence, \(\angle B\) in \(\triangle ABC\) corresponds to \(\angle G\) in \(\triangle EFG\) (because of side - side - side congruence from the markings).

Answer:

B. \(60^{\circ}\)