Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 58.5 degrees. What are the measures of the small and large angle?

1 Answer
Jan 12, 2016

Let the angles be #theta and phi#.

Complementary angles are those whose sum is #90^@#.

It is given that #theta and phi# are complementary .
#implies theta+phi=90^@##...........(i)#

The sum of the measure of the first angle and one-fourth the second angle is 58.5 degrees can be written as a equation.

#theta+1/4phi=58.5^@#

Multiply both sides by #4#.

#implies 4theta+phi=234^@#

#implies 3theta+theta+phi=234^@#

#implies 3theta+90^0=234^@#

#implies 3theta=144^@#

#implies theta=48^@#

Put #theta=48^@# in #(i)#

#implies 48^@+phi=90^@#

#implies phi=42^@#

Therefore, the small angle is #42^@# and larger angle is #48^@#