SOLUTION: two angels are complementary. the measure of the smaller angel is 23 degrees less than the measure of the larger angel. find the measures of the angels.

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Complimentary angles are angles whose sum is 90.
So if x=larger angle
x-23=smaller angle
and:
x + (x-23)=90
2x-23=90
2x=90+23
2x=113
x=56.5 degrees (measure of larger angle)
smaller angle=x-23=56.5-23=33.5 degrees