find angle whose complement is 10 degree less than half of its supplement​

Question

find angle whose complement is 10 degree less than half of its supplement​

in progress 0
1 week 2021-11-25T07:29:00+00:00 1 Answer 0 views 0

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+=+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

+% 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: