Geometry is an important part of mathematics that can help to understand the relationship between shapes and angles. In this homework, we will explore the different relationships between angles and their properties. We will also look at how to calculate the measures of angles in different situations.

## Angle Properties

In geometry, an angle is defined as the space between two lines or sides of a shape. Angles can be measured in degrees and are typically represented by a small square. Each angle has specific properties that define it. These properties include the measure of the angle, its sides, and its vertex. The measure of an angle can either be acute, right, obtuse, or straight. An acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is greater than 90° but less than 180°, and a straight angle is exactly 180°. Knowing the properties of an angle can help us to understand the different relationships between angles.

## Angle Relationships

Angles can be related to each other by the measures of their sides and vertex. For example, two adjacent angles are two angles that share the same vertex, but their sides do not overlap. These two angles are complementary if they add up to 90°, and they are supplementary if they add up to 180°. Another type of relationship between angles is the linear pair. This is when two angles share the same side and add up to 180°. Finally, vertical angles are angles that are opposite each other and have the same measure.

## Calculating Angle Measures

In some cases, we may need to calculate the measure of an angle given certain information. For example, if we know the measure of two of the angles in a triangle, then we can use the triangle angle sum theorem to calculate the measure of the third angle. This theorem states that the sum of the measures of the angles in a triangle is equal to 180°. We can also use the properties of complementary, supplementary, and vertical angles to calculate the measure of an angle if we know the measure of the other angle in the relationship.

In this homework, we explored the different properties of angles and the different relationships between angles. We also discussed how to calculate the measure of an angle given certain information. Understanding the different angle relationships can help us to solve many different types of geometry problems.

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