CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.

검증된 단계별 안내

Identify the given parallel lines, labeled as lines \( m \) and \( n \), and note the transversal line(s) intersecting them.

Recall that when two parallel lines are cut by a transversal, several angle relationships hold, such as corresponding angles being equal, alternate interior angles being equal, and consecutive interior angles being supplementary (adding up to 180 degrees).

Use these angle relationships to set up equations for the numbered angles. For example, if a numbered angle corresponds to another angle on the opposite parallel line, set them equal using \( \text{angle}_1 = \text{angle}_2 \).

If the problem involves supplementary angles (angles on the same side of the transversal inside the parallel lines), use the equation \( \text{angle}_1 + \text{angle}_2 = 180^\circ \) to relate them.

Solve the resulting equations step-by-step to find the measures of the numbered angles, ensuring to substitute known angle values where given.

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주요 개념

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Parallel Lines and Transversals

When two lines are parallel, a transversal crossing them creates specific angle relationships. Understanding how angles correspond, alternate interior, and alternate exterior angles relate is essential to find unknown angle measures.

Angle Relationships

Key angle pairs such as corresponding angles, alternate interior angles, and consecutive interior angles have equal or supplementary measures when lines are parallel. Recognizing these relationships helps determine unknown angles.

Properties of Angles on a Straight Line

Angles that form a linear pair on a straight line sum to 180 degrees. This property is useful for calculating unknown angles when combined with parallel line angle relationships.