Question 217425
"Find the measure of an angle if five times the measure of its complement is 24 less than twice the measure of its supplement" what would the equation be for this?...


Step 1.  Two angles are complementary when they add up to 90 degrees and two angles are supplementary when they add up to 180 degrees


Step 2.  Let x be the angle.


Step 3.  Let 90-x be the complementary angle.


Step 4.  Let 180-x be the supplementary angle.


Step 5.  Let 5(90-x) be five times the complement of the angle.


Step 6.  Let 2(180-x) be twice the measure of its supplement


Step 7.  Let 5(90-x)=2(180-x)-24  since  five times the measure of its complement is 24 less than twice the measure of its supplement
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Step 8.  Then solving the equation of Step 7 {{{5(x-90)=2(180-x)-24}}} will lead to the following steps:


*[invoke explain_simplification "5(90-x)=2(180-x)-24" ]


So x=38 and 90-x=52 and 180-x=142.


Check...{{{5(x-90)=2(x-180)-24}}} if true...5*52=2*142-24...which is a true statement.


Step 9.  ANSWER:  The angle is 38 degrees, its complementary angle is 52 degrees and its supplementary angle is 142 degrees

I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J