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

1. Identify the given angles and note that lines m and n are parallel.
2. Recall that when two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.
3. Use the properties of parallel lines and transversals to set up equations for the marked angles based on their relationships (e.g., corresponding, alternate interior, or consecutive interior).
4. Solve the equations to find the measures of the marked angles.
5. Verify your solutions by checking that all angle relationships (e.g., equal or supplementary) hold true with the calculated measures.

Key Concepts

Parallel Lines and Transversals

When two parallel lines are intersected by a transversal, 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, supplementary, and vertical angles. Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees. Recognizing these relationships helps in solving for unknown angles in geometric figures.

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 knowledge is particularly important when determining the measures of angles formed by intersecting lines or within geometric shapes.