The sum of the measures of two complementary angles is 90°. If one angle measures 18° more than twice the measure of the other, what is the measure of the smaller?

1 Answer
Sep 23, 2016

The measure of the smaller angle is #24# degrees.

Explanation:

Let #x=# the measure of the first angle.
Let #y=# the measure of the complement of the first angle.

One angle, we'll call it #y#, is 18 more than twice the other, #x#.
#y=18+2x#

The sum of complementary angles is #90# degrees.
#x+y=90#

Substituting for #y#...
#x+18+2x=90#

Combining like terms and subtracting 18 from both sides...
#3x+18= color(white)a90#
#color(white)(aa)-18color(white)(a)-18#

#3x=72#

Dividing both sides by 3...
#(3x)/3=72/3#

#x=24#

#y=18+2x=18+2(24)=66#

The smaller of the two angles measures 24 degrees.