Let's highlight the angles we are asked to compare.
We will focus on triangles △ FBA and △ BGC and summarize what we know about the sides of these triangles.
Claim
Justification
FB≅BG
Both segments have a measure of 10.
AB≅CG
Both segments have a measure of 11.
BC< FA
4<10
The information in the table shows that triangles △ FBA and △ BGC have two pairs of congruent sides.
This means that we can apply the Converse of the Hinge Theorem.
BC< FA
⇓
m∠ BGC < m∠ FBA
