#/_DEF# and #/_ABC# are complementary angles? #/_ ABC# is nine times as large as #/_DEF#. What is the measure of each angle?

1 Answer
Jan 2, 2016

#angleABC=81˚,angleDEF=9˚#

Explanation:

The angles are complementary, which means the following statement is true:

#mangleABC+mangleDEF=90color(white)(sssss)# (i)

Since #angleABC# is #9# times greater than #angleDEF#,

#mangleABC=9(mangleDEF)color(white)(sssss)# (ii)

Replace #mangleABC# with #9(mangleDEF)# in (i).

#9(mangleDEF)+mangleDEF=90#
#rArr 10(mangleDEF)=90#
#rArr mangleDEF=9#

Since #mangleABC=9(mangleDEF),# #mangleABC=9(9)=81#.