Angles
4.6 Angles – Cheat Sheet
1. Basic Angle Properties
| Rule | Description | Example |
|---|---|---|
| Sum at a point = 360° | All angles around a point add up to 360° | a + b + c + d = 360° |
| Sum on a straight line = 180° | Adjacent angles forming a straight line | x + y = 180° |
| Vertically opposite angles are equal | When two lines cross, opposite angles match | a = c, b = d |
| Triangle angle sum = 180° | Any triangle’s interior angles total 180° | A + B + C = 180° |
| Quadrilateral angle sum = 360° | Any quadrilateral’s interior angles total 360° | A + B + C + D = 360° |
2. Angles in Parallel Lines
| Property | Description | Diagram Notes |
|---|---|---|
| Corresponding angles | Equal when in matching corners | “F” shape |
| Alternate angles | Equal when opposite sides of transversal | “Z” shape |
| Co-interior angles | Add up to 180° | “C” shape, supplementary |
3. Angle Properties of Polygons
Interior Angle Sum Formula:
Sum = (n − 2) × 180° (where n = number of sides)
Exterior Angle Property:
- Sum of all exterior angles = 360°
- Each exterior angle in a regular polygon = 360° ÷ n
Interior Angle (Regular Polygon):
- Interior = 180° − exterior
4. Examples Table
| Shape | Sides (n) | Interior Sum | Each Interior (regular) | Each Exterior (regular) |
|---|---|---|---|---|
| Triangle | 3 | 180° | 60° | 120° |
| Quadrilateral | 4 | 360° | 90° | 90° |
| Pentagon | 5 | 540° | 108° | 72° |
| Hexagon | 6 | 720° | 120° | 60° |
| Octagon | 8 | 1080° | 135° | 45° |
5. Three-Letter Notation for Angles
- Angle ABC: Vertex is B, so angle is between BA and BC.
- Always write vertex letter in the middle.
6. Sample Problems
Example 1: In a triangle, A = 50°, B = 70°, find C.
- C = 180 − (50 + 70) = 60°
Example 2: Find each interior angle of a regular hexagon.
- Exterior = 360 ÷ 6 = 60°, Interior = 180 − 60 = 120°
Example 3: In parallel lines, corresponding angle to 65° is…
- 65° (equal by corresponding angles rule)