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Math for Grade 7
1 Number Sense and Operations
1-1 Integers
1-1 1 Understanding positive and negative numbers
1-1 2 Comparing and ordering integers
1-1 3 Absolute value
1-1 4 Adding and subtracting integers
1-1 5 Multiplying and dividing integers
1-2 Rational Numbers
1-2 1 Understanding fractions, decimals, and mixed numbers
1-2 2 Comparing and ordering rational numbers
1-2 3 Converting between fractions, decimals, and percents
1-2 4 Adding and subtracting fractions and mixed numbers
1-2 5 Multiplying and dividing fractions and mixed numbers
1-3 Exponents and Roots
1-3 1 Understanding exponents
1-3 2 Laws of exponents
1-3 3 Square roots and cube roots
2 Algebra
2-1 Expressions and Equations
2-1 1 Writing algebraic expressions
2-1 2 Evaluating algebraic expressions
2-1 3 Solving one-step and two-step equations
2-1 4 Solving inequalities
2-2 Patterns and Functions
2-2 1 Identifying and extending patterns
2-2 2 Representing patterns with tables, graphs, and equations
2-2 3 Understanding functions and function notation
3 Geometry
3-1 Shapes and Angles
3-1 1 Classifying polygons
3-1 2 Measuring and drawing angles
3-1 3 Understanding complementary and supplementary angles
3-2 Transformations
3-2 1 Understanding translations, reflections, and rotations
3-2 2 Identifying congruent and similar figures
3-3 Perimeter, Area, and Volume
3-3 1 Calculating perimeter and area of polygons
3-3 2 Understanding and calculating the area of circles
3-3 3 Calculating the volume of rectangular prisms
4 Data and Probability
4-1 Data Representation
4-1 1 Collecting and organizing data
4-1 2 Creating and interpreting bar graphs, line graphs, and pie charts
4-1 3 Understanding mean, median, mode, and range
4-2 Probability
4-2 1 Understanding probability as a ratio
4-2 2 Calculating simple probabilities
4-2 3 Understanding experimental versus theoretical probability
5 Problem Solving and Critical Thinking
5-1 Strategies for Problem Solving
5-1 1 Using logical reasoning and critical thinking
5-1 2 Applying the problem-solving process
5-1 3 Using estimation and approximation
5-2 Real-World Applications
5-2 1 Applying mathematical concepts to real-world scenarios
5-2 2 Understanding the relevance of mathematics in daily life
Understanding Complementary and Supplementary Angles

Understanding Complementary and Supplementary Angles

Key Concepts

1. **Complementary Angles**: Two angles that add up to 90 degrees.

2. **Supplementary Angles**: Two angles that add up to 180 degrees.

Detailed Explanation

Complementary Angles

Complementary angles are two angles whose measures sum to exactly 90 degrees. If the two angles are adjacent (sharing a common vertex and side), they form a right angle. For example, if one angle is 30 degrees, its complementary angle is 60 degrees because \(30 + 60 = 90\).

Supplementary Angles

Supplementary angles are two angles whose measures sum to exactly 180 degrees. If the two angles are adjacent (sharing a common vertex and side), they form a straight line. For example, if one angle is 120 degrees, its supplementary angle is 60 degrees because \(120 + 60 = 180\).

Examples

Example 1: Find the complementary angle of 45 degrees.

Solution: Since complementary angles add up to 90 degrees, the complementary angle is \(90 - 45 = 45\) degrees.

Explanation: Both angles are 45 degrees, forming a right angle.

Example 2: Find the supplementary angle of 135 degrees.

Solution: Since supplementary angles add up to 180 degrees, the supplementary angle is \(180 - 135 = 45\) degrees.

Explanation: The two angles together form a straight line.

Analogies

Think of complementary angles as two pieces of a puzzle that fit together to form a right angle, like the two sides of a right triangle. Supplementary angles, on the other hand, are like two pieces of a straight line that fit together to form a straight path, like the two halves of a straight road.

Practical Application

Understanding complementary and supplementary angles is essential in various real-world scenarios, such as in architecture, design, and navigation. By mastering these concepts, you can better analyze and solve problems involving angles and shapes in everyday life.

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