What you’ll learn
Use adjacent-angle relationships.
Key idea
Nonoverlapping adjacent angles add to their stated combined angle; adjacency alone does not imply180°.
Adjacency alone does not make a straight angle; use the known combined measure and preserve the shared-ray nonoverlap condition.
Worked example
Enter the exact value or ordered values in the format requested below.
Adjacent nonoverlapping AOB=10° and BOC=12° share ray OB; BOC is labeled (2x+4)°. Enter combined AOC measure in degrees.
- Nonoverlapping adjacent angles share a vertex and ray; their combined measure is 10+12=22°.
- If B=(2x+4)°, the record 10+(2x+4)=22 gives x=4; no opposite outer-ray condition is supplied.
Answer: 22
Quick Check
Evaluate a worked attempt at use adjacent-angle relationships, identify the first invalid step, and provide the correction.
Nonoverlapping AOB=10° and BOC=21° labeled (2x+5)° are adjacent. Step1 identifies shared ray OB. Step2 concludes AOC=180° solely because they are adjacent. Locate the first invalid step and correct AOC.