Overview
This lecture explains naming angles, adjacent angles, complementary and supplementary angles, and solving for unknown angles using their properties.
Naming Angles
- An angle can be named using three points, with the vertex in the middle (e.g., ∠ABC, vertex at B).
- If only one angle is at a point, it can be called by its vertex (∠B).
- When two angles share a vertex, numbers may be used for clarity (e.g., ∠B₁, ∠B₂).
Adjacent Angles
- Adjacent angles share a common vertex and one side (arm).
- Examples show angles next to each other (adjacent), sharing a side and vertex.
Perpendicular Lines and Right Angles
- Lines intersecting at 90° are called perpendicular.
- The symbol for a right angle indicates 90°.
Complementary Angles
- Angles that add up to 90° are complementary.
- To find the complement of an angle, subtract it from 90°.
- Examples:
- Complement of 42° = 48° (90° - 42°).
- Complement of 28° = 62° (90° - 28°).
- Complement of x = 90° - x.
- Complement of (90° - a) = a.
Solving Complementary Angle Equations
- If two angles sum to 90°, set up equation: angle 1 + angle 2 = 90°.
- Solve for unknowns using basic algebra.
Supplementary Angles
- Angles that add up to 180° are supplementary.
- To find the supplement of an angle, subtract it from 180°.
- Examples:
- Supplement of 42° = 138° (180° - 42°).
- Supplement of 128° = 52° (180° - 128°).
- Supplement of x = 180° - x.
- Supplement of (90° - a) = 90° + a.
Solving Supplementary Angle Equations
- If two angles sum to 180°, use: angle 1 + angle 2 = 180°.
- Use algebra to solve for unknowns.
Angles on a Straight Line
- The sum of angles on a straight line is always 180°.
Angles in a Triangle
- The sum of the angles in a triangle is always 180°.
- In an isosceles triangle, two angles are equal.
Key Terms & Definitions
- Vertex — the common point where two sides of an angle meet.
- Adjacent angles — angles sharing a vertex and one side.
- Perpendicular lines — lines that intersect at a 90° angle.
- Complementary angles — two angles whose measures add up to 90°.
- Supplementary angles — two angles whose measures add up to 180°.
- Isosceles triangle — a triangle with two equal sides and two equal angles.
Action Items / Next Steps
- Practice finding complements/supplements of given angles.
- Review homework questions involving solving for unknown angles with complementary or supplementary properties.