Answer
$m\angle1=24$
$m\angle2=48$
$m\angle3=72$
$m\angle4=36$
Work Step by Step
Substitute to find the measure of each angle.
$m\angle3=72$
$m\angle2=\frac{2}{3}m\angle3=\frac{2}{3}(72)=48$
$m\angle1=\frac{1}{2}m\angle2=\frac{1}{2}(48)=24$
The angle addition theorem tells us the sum of the 4 angles is 180.
$m\angle1+m\angle2+m\angle3+m\angle4=180$
$24+48+72+m\angle4=180\longrightarrow$ substitution
$144+m\angle4=180\longrightarrow$ simplification
$m\angle4=36\longrightarrow$ subtraction property of equality
