## Geometry: Common Core (15th Edition)

The definition of an angle bisector tells us that: $m\angle ABX=m\angle CBX$ The angle addition postulate tells us that: $m\angle ABX+m\angle CBX=m\angle ABC$ Substitute: $m\angle ABX+m\angle ABX=m\angle ABC$ Combine like terms: $2m\angle ABX=m\angle ABC\longrightarrow$ one student is correct Divide each side by 2: $2m\angle ABX\div2=m\angle ABC\div2$ $m\angle ABX=\frac{1}{2}m\angle ABC\longrightarrow$ the other student is also correct