86. Given: AABC Prove: m/BAC + m LABC + m/BCA 180. %3D Y A Statements Reasons 1) Draw XY through B and parallel to AC. 1) There is exactly one line through a point not on a given line that is parallel to the given line. 2) definition of a linear pair 2) ZXBA and ZABY form a linear pair. 3) mZXBA + mLABY = 180 3) The sum of the measures of the angles in a linear pair is 180°. 4) m LABC+ mLCBY-MLABY 1) angle addition poetulate 5) mZXBA + m ZABC + m ZCBY = 180 5) substitution 6) 6) CBY = ZBCA and LXBA 2 ZBAC 7) definition of congruent angles 7) m ZCBY = m ZBCA and mZXBA m ZBAC 8) mZBAC + m LABC + MZBCA = 180 8) substitution What is the reason for step 6?

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