Complementary angles are two angles that add up to 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always 90 degrees.

- Complementary angles are always acute angles (i.e., angles that are less than 90 degrees).
- Complementary angles can be adjacent (sharing a common vertex and side) or non-adjacent.
- When two angles are complementary, one angle is the complement of the other.

Example 1: If one angle measures 30 degrees, what is the measure of its complement?

To find the complement of an angle, subtract the measure of the given angle from 90 degrees:

Complement = 90° - 30° = 60°

Therefore, the complement of an angle measuring 30 degrees is 60 degrees.

Example 2: Find the measures of two complementary angles if one angle measures 45 degrees.

Since the sum of two complementary angles is 90 degrees, we can find the measure of the second angle using the following equation:

x + 45° = 90°

x = 90° - 45°

x = 45°

So, the measures of the two complementary angles are 45 degrees and 45 degrees.

When studying complementary angles, it's important to remember the following key points:

- Complementary angles add up to 90 degrees.
- Complementary angles are always acute.
- When finding the complement of an angle, subtract its measure from 90 degrees.
- When given one angle, you can find the measure of its complement by subtracting from 90 degrees.

Practice identifying and finding the measures of complementary angles to solidify your understanding of this concept.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.