Question

select the correct answer.
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})
e. ( 120^{circ})

Explanation:

Step1: Use congruent triangle property

Since the triangles are congruent, corresponding angles are equal. In triangle \(ABC\) and triangle \(FEG\), \(\angle A\) corresponds to \(\angle FEG\), \(\angle C\) corresponds to \(\angle F\), and \(\angle B\) corresponds to \(\angle G\).

Step2: Determine the measure of \(\angle B\)

Given \(m\angle G = 60^{\circ}\), and because \(\angle B\) and \(\angle G\) are corresponding angles of congruent triangles.

Answer:

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