## Elementary Geometry for College Students (6th Edition)

measure of arc $CA=160^{\circ}$
The measure of an entire circle is $360^{\circ}$. If you add the three arcs together...$AB+BC+CA$ you have the entire circle. So... arc $AB=2x$, arc $BC=3x$, and arc $AC=4x$. $2x+3x+4x=360$ combine like terms... $9x=360$ Divide both sides by 9... $x=40$ Plug $x=40$ into the $4x$ (the measure of arc $CA$) and the measure of arc $CA=160^{\circ}$.