Angle Addition Postulate

Overview

• Discusses what the Angle Addition Postulate is, its meaning, and its applications.

Key Concepts

• Angle Addition Postulate: If you have an angle and a point inside it, you can split the angle into two smaller angles.
• Notation: Name angles using three letters, with the vertex second.
  • Example: For angle ABC, it can be named as ABF or FBC, with B always in the middle.

Definitions

• Interior Point: A point inside the angle that allows for the construction of a ray that divides the angle into two smaller angles.
• Measure of Angles: Notate the measures as little 'm'.
  • Formula: m(ABF) + m(FBC) = m(ABC) (Measure of smaller angles equals measure of the whole angle)
• Comparison to Segment Addition Postulate: Similar concepts apply for segments and angles; part plus part equals whole.

Example Problem 1

• Given:
  • m(TMS) = 12 degrees
  • m(LMT) = 39 degrees
• Find m(LMS):
  • Setup: m(LMS) + m(SMT) = m(LMT)
  • Substituting values: m(LMS) + 12 = 39
  • Solution: m(LMS) = 39 - 12 = 27 degrees
  • Check: 27 + 12 = 39 (correct)

Example Problem 2

• Given:
  • m(MNP) = 3x
  • m(PNR) = 2x - 6
  • m(MNR) = 44 degrees
• Setup: m(MNP) + m(PNR) = m(MNR)
  • Substitute values: 3x + (2x - 6) = 44
  • Simplify: 5x - 6 = 44
  • Solve: 5x = 50 → x = 10
• Find measures of angles:
  • m(MNP) = 3(10) = 30 degrees
  • m(PNR) = 2(10) - 6 = 14 degrees
• Check: 30 + 14 = 44 (correct)

Conclusion

• Importance of checking answers in angle problems.
• Understanding the structure of angle relationships assists in solving for missing measures.
• Encouragement to practice and apply these concepts.