Question

step angle reason
1 m∠bfc = 75° given
2 m∠gfc = 38° given
3 m∠fbc = 67° select a reason
sum of angles in a triangle
vertical angles
linear pair (or triple)
congruent angles
sum of angles in a triangle
sum of angles in a quadrilateral
base angle of an isosceles triangle
angle bisector definition
corresponding angles
alternate interior angles
alternate exterior angles
same - side interior angles
angle addition postulate
angle subtraction postulate
perpendicular lines form right angles
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In a triangle with angles \(m\angle BFC\), \(m\angle GFC\) and \(m\angle FBC\), we know that \(m\angle BFC + m\angle GFC+m\angle FBC=180^{\circ}\) (assuming the relevant triangle situation).

Step2: Substitute the given angle values

We are given \(m\angle BFC = 75^{\circ}\) and \(m\angle GFC = 38^{\circ}\). Let \(x=m\angle FBC\). Then \(75 + 38+x=180\).

Step3: Solve for \(x\)

First, add 75 and 38: \(75 + 38=113\). Then the equation becomes \(113+x = 180\). Subtract 113 from both sides: \(x=180 - 113=67^{\circ}\).

Answer:

\(67\)