What you’ll learn
Prove vertical-angle theorem.
Key idea
A linear pair supplies a supplementary total, not equality to the adjacent angle.
Addition does not cancel positive shared angle terms; supplementary does not mean equal to the supplement.
Worked example
Complete missing statements or reasons in a proof for 'Prove vertical-angle theorem'.
Two lines intersect. Angles 1 and 3 are opposite; each forms a linear pair with angle 2, whose measure is 85 degrees. Proof already gives m1+m2=180 and m3+m2=180. Complete its final statement AND reason.
- Linear pairs give m1+m2=180 and m3+m2=180.
- Equate these totals and subtract the SAME m2=85; m1=m3=95 degrees. Adding would retain twice m2, not cancel it.
Answer: m1=m3=95 degrees — equal totals minus common m2 leave equal remainders.
Quick Check
Complete missing statements or reasons in a proof for 'Prove vertical-angle theorem'.
Two lines intersect. Angles 1 and 3 are opposite; each forms a linear pair with angle 2, whose measure is 50 degrees. Proof already gives m1+m2=180 and m3+m2=180. Complete its final statement AND reason.