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

검증된 단계별 안내

Identify the given information: lines \(m\) and \(n\) are parallel, and there are marked angles formed by a transversal intersecting these parallel lines.

Recall the key angle relationships when a transversal crosses parallel lines: corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to \(180^\circ\)).

Use the given angle measures or expressions to set up equations based on these relationships. For example, if an angle on line \(m\) is given, find the corresponding angle on line \(n\) by setting them equal.

Solve the equations step-by-step to find the measure of each marked angle, ensuring to apply the correct angle relationship depending on their positions (corresponding, alternate interior, or consecutive interior).

Double-check your answers by verifying that the angles satisfy the properties of parallel lines and the sum of angles around a point or on a straight line where applicable.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Parallel Lines and Transversals

When two parallel lines are cut by a transversal, several angle relationships are formed, such as corresponding, alternate interior, and alternate exterior angles. These relationships help determine unknown angle measures by establishing equality or supplementary conditions.

Angle Relationships

Key angle pairs include corresponding angles (equal), alternate interior angles (equal), and consecutive interior angles (supplementary). Understanding these relationships allows you to set up equations to find unknown angles when parallel lines are involved.

Using Algebra to Solve for Angles

Often, marked angles are expressed in terms of variables. By applying angle relationships and setting up equations, you can solve for these variables to find the exact measure of each angle. This combines geometric reasoning with algebraic manipulation.