The sum of the measures of two complementary angles is 90°. If one angle measures 21° more than twice the measure of the​ other, find the measure of the smaller angle?

1 Answer
Jim G.
Jan 13, 2018

#"smaller angle "=23^@#

Explanation:

#"let the 2 angles be "x" and "ycolor(white)(x);xx>y#

#"then "x+y=90to(1)#

#"and "x=2y+21larrcolor(blue)"21 more than twice the other"#

#"substitute "x=2y+21" into equation "(1)#

#2y+21+y=90#

#rArr3y+21=90#

#"subtract 21 from both sides"#

#3ycancel(+21)cancel(-21)=90-21#

#rArr3y=69#

#"divide both sides by 3"#

#(cancel(3) y)/cancel(3)=69/3#

#rArry=23#

#"substitute "y=23" in "(1)#

#x+23=90rArrx=67#

#"the 2 angles are "23^@" and "67^@#

#color(blue)"As a check"#

#(2xx23)+21=46+21=67larr" True"#

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