Question

question in the diagram below, ad || eg. angle bfc = 75°. angle gfc = 38°. find m∠fbc. select a reason 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

Explanation:

Step1: Recall angle - addition postulate

The angle - addition postulate states that if we have two adjacent angles, the measure of the larger angle is the sum of the measures of the two smaller adjacent angles. Here, $\angle BFC=\angle BFG+\angle GFC$. We want to find $\angle BFG$, and we know that $\angle BFC = 75^{\circ}$ and $\angle GFC=38^{\circ}$.

Step2: Rearrange the formula

We can rewrite the angle - addition formula as $\angle BFG=\angle BFC-\angle GFC$.

Step3: Substitute the values

Substitute $\angle BFC = 75^{\circ}$ and $\angle GFC = 38^{\circ}$ into the formula: $\angle BFG=75^{\circ}-38^{\circ}=37^{\circ}$.

Answer:

The measure of $\angle BFG$ is $37^{\circ}$ and the reason is Angle subtraction postulate.