Answer
$m\angle DEC=142$
$m\angle CEF=38$
Work Step by Step
Since $\angle DEF$ is a straight angle, $m\angle DEF=180$.
$m\angle DEC + m\angle CEF = m\angle DEF\longrightarrow$ Angle Addition Postulate
$(11x-12)+(2x+10)=180\longrightarrow$ substitute
$13x-2=180\longrightarrow$ combine like terms
$13x-2+2=180+2\longrightarrow$ add 2 to each side
$13x=182\longrightarrow$ simplify
$13x\div13=182\div13\longrightarrow$ divide each side by 13
$x=14\longrightarrow$ simplify
Substitute to find the measurements.
$m\angle DEC=11x-12=11(14)-12=154-12=142$
$m\angle CEF=2x+10=2(14)+10=28+10=38$
