Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Verified step by step guidance

1. Identify the given information: m and n are parallel lines, and there are marked angles formed by a transversal intersecting these parallel lines.
2. Recall the properties of parallel lines and transversals: Corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.
3. Determine which angles are marked and their relationships using the properties of parallel lines and transversals.
4. Use the relationships to set up equations for the marked angles. For example, if two angles are corresponding, set them equal to each other.
5. Solve the equations to find the measure of each marked angle, ensuring to check that all angle relationships are satisfied.

Key Concepts

Parallel Lines and Transversals

When two lines are parallel, and a transversal crosses them, several angle relationships are formed. Corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Understanding these relationships is crucial for finding unknown angles when given certain marked angles.

Angle Relationships

In geometry, angles can be classified into various relationships such as complementary (sum to 90 degrees), supplementary (sum to 180 degrees), and vertical angles (equal in measure). Recognizing these relationships helps in solving for unknown angles when certain angles are provided, especially in configurations involving parallel lines.

Angle Measurement

Angle measurement is typically expressed in degrees or radians. In trigonometry, understanding how to convert between these units and apply them in calculations is essential. This includes using the properties of angles formed by intersecting lines, which is fundamental in determining the measures of marked angles in geometric figures.