#### Answer

C

#### Work Step by Step

Let A be the angle, let C be the measure of its complement, and let S be the measure of its supplement.
$C+S=114\longrightarrow$ given
$(m\angle A+C)+(m\angle A+S)=90+180\longrightarrow$ definition of complement and supplement
$2m\angle A+C+S=270\longrightarrow$ combine like terms
$2m\angle A+114=270\longrightarrow$ substitution
$2m\angle A=156\longrightarrow$ subtraction property of equality
$m\angle A=78\longrightarrow$ division property of equality