SOLUTION: One of two complementary angles added to one-half the other yields 72.Find half the measure of the larger angle.

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Question 215119: One of two complementary angles added to one-half the other yields 72.Find half the measure of the larger angle.
Found 2 solutions by RAY100, drj:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Let x & y be complementary angles,,,x+y=90,,,or,,,y=90-x
.
x +y/2 = 72,,,,,,substitute
.
x+(90-x)/2 =72
.
x+45-x/2 = 72
.
+x/2 = 72-45 = 27
.
x=54,,,,,,,,y=90-54=36
.
check,,,,,54 + 18 = 72,,,,,ok
.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One of two complementary angles added to one-half the other yields 72. Find half the measure of the larger angle.

Step 1. Two angles are complementary when they add up to 90 degrees.

Step 2. Let x be one angle and 90-x be its complementary angle.

Step 3. Let x/2 be one-half of one complementary angle

Step 4. One of two complementary angles added to one-half the other yields 72. Translating this problem into an equation and solving yields

x%2F2%2B90-x=72

Multiply by 2 to both sides of equation to get rid of denominator.

2%2A%28x%2F2%2B90-x%29=2%2A72

x%2B180-2x=144

180-x=144

Add x-144 to both sides to solve for x.

180-x%2Bx-144=144%2Bx-144

36=x

Step 5. The complementary angle of 36 is 90-36=54. One-half of 54 is 27.

Step 6. ANSWER: Half the measure of the larger angle is 27 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