The Angle Addition Postulate
Just like segments can be split into parts that add up, so can angles — the Angle Addition Postulate is the angular version of Segment Addition.
Introduction
If a ray splits an angle into two smaller angles, their measures add up to the whole — no overlap, no gaps. This is the Angle Addition Postulate.
Past Knowledge
Naming angles (1.3.1). Segment Addition (1.2.1).
Today's Goal
Apply the Angle Addition Postulate to find unknown angle measures.
Future Success
Complementary/supplementary angles (1.3.3) and proofs involving angle relationships.
Key Concepts
Angle Addition Postulate
If ray is in the interior of , then:
Think: Part + Part = Whole
This is exactly the same logic as Segment Addition — the two smaller angles are “parts” that compose the larger “whole” angle.
Worked Examples
Finding a Missing Angle
and . is in the interior. Find .
Answer:
Algebra with Angle Addition
, , . Find .
Answer: , so and .
Common Pitfalls
Ray Must Be in the Interior
The Angle Addition Postulate only applies when the dividing ray is inside the angle, not outside it.
Real-Life Applications
Pizza Slicing
Cutting a pizza into slices splits the full 360° angle at the centre. Each cut creates a ray, and the Angle Addition Postulate guarantees the slice angles sum to 360°. Eight equal slices = 45° each.
Practice Quiz
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