Question 342243
The sum of the measures of two complementary angles exceeds the difference of the measures of their supplements by 32 degrees.  Find the measure of each angle.


Let the 1st angle be A, then the 2nd angle or the complement of the 1st angle = 90 – A


The supplement of the 1st angle would then be 180 – A, and the supplement of the 2nd angle = 180 – (90 – A), or 180 – 90 + A, or 90 + A

Now, since the sum of the measures of the two complementary angles exceeds the difference of the measures of their supplements by 32 degrees, then we’ll have:


A + 90 – A = 180 – A – (90 + A) + 32

90 = 180 – A – 90 – A + 32


90 = 122 – 2A


2A  = 122 – 90___2A = 32


A, or 1st angle = {{{32/2}}} = {{{highlight_green(16^o)}}}, and the measure of the 2nd angle = 90 – 16, or {{{highlight_green(74^o)}}}


-----------
Check
-----------

The sum of the complement angles or 90 (16 + 74), exceeds the difference of their complements, 164 (180 - 16) and 106 (180 - 74) or 58 (164 - 106) by 32.


Send comments and “thank-yous” to MathMadEzy@aol.com