## Geometry: Common Core (15th Edition)

$m\angle1=24$ $m\angle2=48$ $m\angle3=72$ $m\angle4=36$
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