Question 222800
Find the degree measure of an angle whose complement is 25 percent of its supplement.


Step 1.  Complementary angles means two angles add up 90 degrees.


Step 2. Supplementary angles means two angles add up 180 degrees.


Step 3.  Let x be the angle


Step 4.  Let 90-x be the complementary angle


Step 5.  Let 180-x be the supplementary angle.


Step 6.  Let 25% be 1/4=0.25 by definition


Step 7.  Then {{{90-x=(180-x)/4}}} since measure of an angle whose complement is 25 percent of its supplement.


Step 8.  Solving equation in Step 7 yields the following steps...


{{{90-x=(180-x)/4}}} 


Multiply by 4 to both sides of the equation


{{{4(90-x)=180-x}}}


{{{360-4x=180-x}}}


Add 4x-180 to both sides of the equation


{{{360-4x+4x-180=180-x+4x-180}}}


{{{180=3x}}}


Divide by 3 to both sides of the equation


{{{180/3=3x/3}}}


{{{x=60}}}  Then {{{90-x=30}}} and {{{180-60=120}}} and the complementary angle of 30 degrees is equal to 25 percent of the supplementary angle of 120 degrees


Step 9.  ANSWER:  The angle is 60 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J