Answer
x=18
Work Step by Step
Angle Addition Postulate:
$m\angle AOB+m\angle BOC+ m\angle COD=m\angle AOD$
Substitute the given values. Remember $\angle AOB\cong\angle COD$
$28+(3x-2)+28=6x$
Combine like terms.
$54+3x=6x$
Subtract 3x from each side.
$54+3x-3x=6x-3x$
$54=3x$
Divide each side by 3.
$54\div3=3x\div3$
$18=x$
Substitute for x to find the angle measures.
$m\angle BOC=3x-2=3(18)-2=54-2=52$
$m\angle AOD=6x=6(18)=108$
Check the angle measures.
$28+52+28\overset?=108$
$80+28\overset?=108$
$108=108\checkmark$
