📐 Geometry · Basics
Angle Relationships cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The patterns
- Complementary: two angles, sum 90° (C for Corner)
- Supplementary: two angles, sum 180° (S for Straight)
- Linear pair: adjacent angles that form a line, sum 180°
- Vertical angles: opposite angles at a crossing, equal
- Around a point: sum 360°
- Bisector: splits an angle into two equal angles
Notation
- ∠ABC is the angle. The vertex B is the middle letter.
- m∠ABC is its measure, a number of degrees
- m∠ABC = m∠DEF means the two angles have equal measures
Solve an angle equation (N-E-S-C)
- Name the pattern
- Equation: add to the total, or set equal
- Solve for x
- Check: substitute, find every angle, and make sure each is positive
Watch out
- Do not assume equal or right angles from the look of a diagram
- Adjacent does not mean supplementary
- Vertical angles are equal, not supplementary
- Complement of x is 90 − x; supplement is 180 − x
Formulas
- Complementary: m∠1 + m∠2 = 90°
- Supplementary or linear pair: m∠1 + m∠2 = 180°
- Vertical angles: m∠1 = m∠3 for opposite angles
- Angles around a point: sum of the angles = 360°
- Bisector: m∠ABC = 2 × m∠ABD
- Complement and supplement of $x°$: (90 − x)° and (180 − x)°
Angle Relationships cheat sheet from HighSchoolQ.com, for personal study use.