SOLUTION: if measure of the complement of the an angle is 10 less than half the measure of the supplement of the same angle find the measure of the angle, its complement, and its supplement.

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Question 934034: if measure of the complement of the an angle is 10 less than half the measure of the supplement of the same angle find the measure of the angle, its complement, and its supplement.
Found 2 solutions by Techpriest, MathTherapy:
Answer by Techpriest(29) About Me  (Show Source):
You can put this solution on YOUR website!
We know that complementary angles are 90 degree.
We know that supplementary angles are 180 degree.
Based on the statement you have provided we can setup an equation such as:
+90+=+%281%2F2%29%28180-x%29+%2B+x+-+10+
We can now solve for x.
+90+-+x+=+%281%2F2%29%28180-x%29+%2B+x+-+10+-+x+ Subtraction Property of Equality
+90+-+x+%2B+10+=+%281%2F2%29%28180-x%29+-+10+%2B+10+ Addition Property of Equality
+90+-+x+%2B+10+=+90-%281%2F2%29x+ Distribution Property
+100+-+x+=+90-%281%2F2%29x+ Combine Like Terms
+100+-+90+-+x+=+90+-+90+-+%281%2F2%29x+ Subtraction Property of Equality
+10+-+x+%2B+x+=+-%281%2F2%29x+%2B+x+ Addition Property of Equality
+%282%2F1%2910+=+1%2F2x%282%2F1%29+ Multiplication Inverse or Reciprocal
+20+=+x+
The angle is x.
Since we know that complement angles add up to 90 degree. We can assume that:
+20+%2B+y+=+90+
+20+-+20+%2B+y+=+90+-+20+
+y+=+70+
Since we know that supplement angles add up to 180 degree. We can assume that:
+20+%2B+z+=+180+
+20+-+20+%2B+y+=+180+-+20+
+z+=+160+
Can we check that it is correct?
Of course, since we know that z is the supplementary angles and it is 160, we can plug in for the first equation.
+90+=+%281%2F2%29%28160%29+%2B+x+-+10+ Substitution
+90+=+80+%2B+x+-+10+ Simplify
+90+=+70+%2B+x+ Combine Like Terms
+90+-+70+=+70+-+70+%2B+x+ Subtraction Property of Equality
+20+=+x+
We get the same answer and now we know that the angle is 20 degree, the complement is 70 degree and the supplement is 160 degree.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

if measure of the complement of the an angle is 10 less than half the measure of the supplement of the same angle find the measure of the angle, its complement, and its supplement.
Let measure of angle be A

Then its complement = 90 – A, and its supplement = 180 – A

Therefore, 90 – A = ½(180 – A) – 10________90+-+A+=+%28180+-+A%29%2F2+-+10

180 – 2A = 180 – A – 20 ------ Multiplying by LCD, 2 

– 2A + A = 160 – 180 

- A = - 20

A, or measure of angle = %28-+20%29%2F%28-+1%29, or highlight_green%2820%5Eo%29

Measure of angle’s complement: 90 – 20, or highlight_green%2870%5Eo%29

Measure of angle’s supplement: 180 – 20, or highlight_green%28160%5Eo%29

You can do the check!! 

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