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angle REC and angle BIG are added togehter to create 180 degrees, what is the reson for this?

angle REC and angle BIG added together equal 180 degrees, what is the reson (postulate, definition, or theorem) for this?

The angles are added together to form a straight line.  Euclid's prop 13 theorem  When a straight line that stands on another straight line makes two angles, either it makes two right angles, or it makes angles that together are equal to two right angles.

This question is worded a little funny, I agree with the other tutorâ€™s post.

Definition Supplementary Angles: two angles when added together total 180 degrees

There is not a way for me to sketch in this post so I will try to be specific with my wording.

If you have angle REC, then E is the center of this angle with segments ER and EC.

Angle BIG would similarly have a center at I, with segments IB and IG.

If you are to put the segments EC and IB right next to each other you should now be able to see that you will have a straight line (180 degrees) connecting R to G.

I can't quite make sure that I picture twe image correctly, but normally supplemental angles add up to 180 degrees. It is a definition of supplemental angles, even though there might be a postulate about it.