Answer
a) x=36
b) $\angle ABC$ is acute. $\angle CBD$ is obtuse.
Work Step by Step
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
