Angle relationships - SAT Math

Описание: *CORE CONCEPT:*
Angle relationships involve understanding how different angles interact, including complementary and supplementary angles, and applying properties of angles formed by parallel lines and transversals.

*TOPICS COVERED:*
When to use complementary angles: Identify angles that sum to 90°.
When to use supplementary angles: Identify angles that sum to 180°.
How to use properties of parallel lines: Recognize corresponding, alternate interior, and same-side interior angles when a transversal crosses parallel lines.
Level: B2

*EXAMPLE SENTENCES:*
Example 1: If angle A and angle B are complementary and angle A = 30°, find angle B.
Example 2: In a diagram, angle 1 and angle 2 are alternate interior angles, and angle 1 = 75°. Find angle 2.
Example 3: If two angles are supplementary and one angle is 2x + 10° while the other is x + 20°, find x.

*GRAMMAR RULES:*
Complementary angles → sum to 90°.
Supplementary angles → sum to 180°.
Alternate interior angles → are equal when formed by a transversal and parallel lines.
Set up equations → translate angle relationships into equations to solve for unknown angles.

*COMMON ERRORS:*
Wrong: If angle A = 40° and angle B is said to be supplementary, then angle B = 140° → Right: angle B = 180° - 40° = 140°.
Wrong: If angle 1 = 50° and angle 2 is incorrectly stated as 50° when they are supposed to be supplementary → Right: angle 2 = 180° - 50° = 130°.

*STUDENT QUESTIONS:*
How do I identify complementary and supplementary angles?
When to use properties of parallel lines in angle problems?
Is my calculation for angle B correct if angle A is 30°?
What's the difference between complementary and supplementary angles?
How do I set up equations for angle relationships?

*KEY CONCEPTS:*
Angle relationships, complementary angles, supplementary angles, parallel lines, transversals, B2 level, geometry.

Key concepts (auto-augmented): sat math, B2 level, problem solving, mathematical reasoning