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 corresponding, alternate interior, or consecutive interior based on their positions relative to the parallel lines and the transversal.
4. Use the properties of these angles to set up equations. For example, if two angles are corresponding, set them equal to each other. If they are consecutive interior angles, set their sum equal to 180 degrees.
5. Solve the equations to find the measures of the marked angles, ensuring to check each step for consistency with the properties of parallel lines and transversals.

Key Concepts

Parallel Lines and Transversals

When two lines are parallel, and a transversal crosses them, several angle relationships are established. Corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Understanding these relationships is crucial for solving problems involving parallel lines and angles.

Angle Relationships

In geometry, angles formed by intersecting lines have specific relationships that can be used to find unknown measures. For example, vertical angles are equal, and the sum of angles on a straight line is 180 degrees. Recognizing these relationships helps in calculating the measures of marked angles effectively.

Angle Measurement

Angle measurement is typically expressed in degrees, where a full rotation is 360 degrees. In problems involving parallel lines and angles, it is essential to apply the correct measurement techniques to determine the size of each angle accurately. This includes using known angle measures to find unknown ones through addition or subtraction.