What is the measure of two complementary angles if the measure of the larger angles is 12 more than twice the measure at the smaller angle?

1 Answer
Ms. Worth
Nov 28, 2017

The smaller angle is #26^@#
The larger angle is #64^@#

Explanation:

Let #x# equal the number of degrees in the smaller angle.

Smaller angle. . . . . . . . . . #x# #larr# smaller angle
Twice that measure . . . #2x#
12 more than that . . . . . #2x + 12# #larr# larger angle

Together, these two angles add up to #90^@#

[small angle] plus [large angle ] #= 90#
#[ . . . ( x ) . . .] . + . [ .(2x + 12) ] = 90#

#(x) + (2x + 12) = 90#
Solve for #x#, already defined as "the number of degrees in the smaller angle."

1) Combine like terms
#3x + 12 = 90#

2) Subtract 12 from both sides to isolate the #3x# term
#3x = 78#

3) Divide both sides by #3# to isolate #x#, already defined as "the number of degrees in the smaller angle"
#x = 26# #larr# the number of degrees in the smaller angle

Answer:
The smaller angle is #26^@#
So the larger angle must be #64^@#

Check
#26# plus #12# more than (#2# times #26#) should equal #90#
#26 + 2(26) + 12# should equal #90#
#26 + 52 + 12# should equal #90#
#26 + 64# should equal #90#
#90# does #= 90#
Check!

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