📐 Angle Relationships

What are Complementary Angles?
Two angles are complementary if their measures add up to 90°.
• Each angle is called the complement of the other
• They don't have to be adjacent (next to each other)

Example: 30° + 60° = 90° → Complementary
What are Supplementary Angles?
Two angles are supplementary if their measures add up to 180°.
• Each angle is called the supplement of the other
• They don't have to be adjacent

Example: 110° + 70° = 180° → Supplementary

Vertical Angles
When two lines intersect, they form two pairs of vertical angles.
Vertical angles are ALWAYS EQUAL!
┌─────┐
│ │
───┼─────┼───
│ │
└─────┘

Angle 1 = Angle 3 (vertical)
Angle 2 = Angle 4 (vertical)Adjacent Angles on a Line
When two angles share a vertex and a side, and together form a straight line, they are adjacent and supplementary (sum to 180°).
/
/ 1│
/ │
/ │
└─────┘
2

Angles 1 and 2 are adjacent and form a linear pair
1 + 2 = 180°

Triangle Angle Sum Theorem
The sum of the three interior angles in ANY triangle is always 180°!
∠A + ∠B + ∠C = 180°Why is this true? If you tear off the corners of a triangle and put them together, they form a straight line (180°).
Finding Missing Angles:
• If you know two angles, subtract their sum from 180°