#### Answer

60

#### Work Step by Step

Let $\angle A$ be the angle in question. Let C be the measure of its complement and S be the measure of its supplement.
$S=4C\longrightarrow$ given
$m\angle A+S=180\longrightarrow$ definition of supplementary
$m\angle A=180-S\longrightarrow$ subtraction property of equality
$m\angle A+C=90\longrightarrow$ definition of complementary
$m\angle A=90-C\longrightarrow$ subtraction property of equality
$180-S=90-C\longrightarrow$ transitive property of equality
$180-4C=90-C\longrightarrow$ substitution
$180=90+3C\longrightarrow$ addition property of equality
$90=3C\longrightarrow$ subtraction property of equality
$30=C\longrightarrow$ division property of equality
Substitute to find the measure of the angle.
$m\angle A + C=90\longrightarrow$ definition of complementary
$m\angle A+30=90\longrightarrow$ substitution
$m\angle A=60\longrightarrow$ subtraction property of equality