find angle whose complement is 10 degree less than half of its supplement
Answers
Answer:
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 + and + = + 90+
+20 + - + 20 +% 2B + y + = + 90 + - + 20+
+ and + = + 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
Step-by-step explanation:
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