Overview
This lecture covers how to name angles, identify adjacent, complementary, and supplementary angles, and solve for unknown angles using angle relationships.
Naming Angles
- Angles can be named using three letters (e.g., angle ABC) with the vertex letter in the middle.
- If only one angle exists at a vertex, it can be named by that vertex alone (e.g., angle B).
- When multiple angles share a vertex, subscripts or numbers can be used (e.g., angle B₁, angle B₂).
Adjacent Angles
- Adjacent angles share a common vertex and one side.
- Examples show two angles at the same point sharing a side.
Right Angles and Perpendicular Lines
- A right angle measures 90° and is shown by a box symbol.
- Perpendicular lines intersect at 90° and are notated as AB ⟂ CD.
Complementary Angles
- Complementary angles add up to 90°.
- To find the complement of an angle, subtract it from 90°: complement of x = 90° – x.
- Example: Complement of 42° is 48°, complement of 28° is 62°.
- If an angle is (90° – a), its complement is a.
Solving Complementary Angles Problems
- If two angles are complementary, their sum is 90°.
- Set up equations and solve for unknowns accordingly.
Supplementary Angles
- Supplementary angles add up to 180°.
- To find the supplement of an angle, subtract it from 180°: supplement of x = 180° – x.
- Example: Supplement of 42° is 138°, supplement of 128° is 52°.
- Supplement of (90° – a) is (90° + a).
Solving Supplementary Angles Problems
- Adjacent angles on a straight line are supplementary.
- Set up equations based on the sum being 180° and solve for the unknown.
Angles in Triangles
- The angles in a triangle always add up to 180°.
- In isosceles triangles, two angles are equal.
- Use known angles and triangle properties to solve for unknown angles.
Key Terms & Definitions
- Angle — A figure formed by two rays sharing a common vertex.
- Adjacent Angles — Angles that share a vertex and a side.
- Right Angle — An angle of 90°.
- Perpendicular Lines — Lines that intersect at 90°.
- Complementary Angles — Angles whose measures add up to 90°.
- Supplementary Angles — Angles whose measures add up to 180°.
- Isosceles Triangle — A triangle with two equal angles.
Action Items / Next Steps
- Review and practice finding complements and supplements of given angle values.
- Solve provided angle equations for unknowns.
- Prepare for the test by studying angle relationships and examples.