## Geometry: Common Core (15th Edition)

a) x=36 b) $\angle ABC$ is acute. $\angle CBD$ is obtuse.
Use the definition of a linear pair: $m\angle ABC+m\angle CBD=180$ Substitute: $2x+3x=180$ Combine line terms: $5x=180$ Divide each side by 5: $5x\div5=180\div5$ $x=36$ Substitute to find the measures: $m\angle ABC=2x=2(36)=72$; acute, since the angle is between and 90 $m\angle CBD=3x=3(36)=108$; obtuse since the angle is between 90 and 180