Question 208310This question is from textbook geometry
: the means of two complementary angles are 16z-9 and 4z+3.find the measures of the angles This question is from textbook geometry
You can put this solution on YOUR website! the means of two complementary angles are 16z-9 and 4z+3.find the measures of the angles
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If two angles are "complementary", the sum of the two angles MUST equal 90 degrees.
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(16z-9) + (4z+3) = 90
16z-9 + 4z+3 = 90
16z+4z+3-9 = 90
20z-6 = 90
20z = 96
z = 96/20
z = 24/5
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Therefore, the two angles are:
16z-9 = 16(24/5)-9 = 16(4.8)-9 = 76.8-9 = 67.8 degrees
4z+3 = 4(24/5)+3 = 4(4.8)+3 = 19.2+3 = 22.2 degrees
The 'means of two complementary angles' doesn't make any sense in this context. Namely, when you give two values implying that each angle has its own individual mean. A 'mean' when applied to angles only makes sense when you have two or more angles and a single mean that is the average (sort of) of all of them.
I suspect what you meant was: "The measures of two complementary angles are 16z-9 and 4z+3. Find the measures of the angles." You also don't mention whether you are working in degrees or radians. I'll presume degrees. If my assumptions are correct, proceed as follows:
Two angles are complementary if and only if the sum of their measures is 90 degrees. So:
Solve for , then substitute this value back into each of the individual expressions for the measures of the two angles. Check your work by adding the two results to ensure that the sum is 90.
