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 properties of angles formed by a transversal with parallel lines, such as corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles, which are either equal or supplementary.

Use the fact that corresponding angles are equal when two lines are parallel, so if you know one angle, you can find its corresponding angle on the other parallel line.

Apply the property that alternate interior angles are equal, which helps find unknown angles inside the parallel lines but on opposite sides of the transversal.

If necessary, use the fact that angles on a straight line sum to \(180^\circ\) to find missing angles by setting up equations and solving for the unknown angle measures.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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Parallel Lines and Transversals

When two parallel lines are cut by a transversal, several angle relationships are formed, such as corresponding angles, alternate interior angles, and consecutive interior 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 algebraic terms. By applying angle relationships from parallel lines and transversals, you can form equations and solve for the variable, then substitute back to find the exact angle measures.