## Geometry: Common Core (15th Edition)

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