Question

1. find ( mangle fab ).

Explanation:

Step1: Identify the theorem

Since \( BA \parallel \) (wait, actually, \( \angle B = 3x + 2 \) and \( \angle FAB \) is an exterior angle? Wait, no, looking at the triangle, \( \angle FAB \) is an exterior angle to triangle \( ABC \), so by the exterior angle theorem, \( \angle FAB=\angle B + \angle C \). Wait, no, actually, \( BA \) is a segment, and \( \angle FAB \) and \( \angle BAC \) are supplementary? Wait, no, maybe \( BA \) is parallel to some line? Wait, no, the diagram: \( \angle FAB \) is \( 13x - 3 \), and \( \angle B = 3x + 2 \), \( \angle C = 55^\circ \). Wait, maybe \( BA \) is parallel to \(... \) No, actually, \( \angle FAB \) is an exterior angle of triangle \( ABC \), so \( \angle FAB=\angle B+\angle C \). Wait, that would be \( 13x - 3=(3x + 2)+55 \). Let's check that.

Step2: Solve for x

Set up the equation: \( 13x - 3 = 3x + 2 + 55 \)
Simplify right side: \( 3x + 57 \)
Subtract \( 3x \) from both sides: \( 10x - 3 = 57 \)
Add 3 to both sides: \( 10x = 60 \)
Divide by 10: \( x = 6 \)

Step3: Find \( m\angle FAB \)

Substitute \( x = 6 \) into \( 13x - 3 \): \( 13(6)-3 = 78 - 3 = 75^\circ \)

Answer:

\( 75^\circ \)