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

1. Identify the given angles and any relationships between them, such as corresponding angles, alternate interior angles, or consecutive interior angles, due to the parallel lines m and n.
2. Use the fact that parallel lines cut by a transversal create equal corresponding angles and supplementary consecutive interior angles.
3. Set up equations based on these relationships to express the unknown angles in terms of known angles.
4. Solve the equations to find the measures of the unknown angles.
5. Verify your solutions by checking that all angle relationships hold true, ensuring the sum of angles around a point is 360 degrees and the sum of angles in a triangle is 180 degrees, if applicable.

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 various configurations.

Angle Notation and Measurement

Angles are often denoted using symbols such as <A, <B, etc., and their measures are expressed in degrees or radians. Understanding how to read and interpret angle notation is essential for accurately determining the measures of marked angles in geometric figures, especially when working with parallel lines and transversals.