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Solving Angle Measures in Parallel Lines Cut by Transversals

This guide focuses on calculating the measures of angles formed by parallel lines intersected by transversals. Several scenarios are presented where users must determine angle measures using known values and properties of parallel lines. The problems include various configurations with parallel lines such as XY || JK, ST || QG, and MN || KL, alongside transversal lines. Readers will learn the application of angle relationships, including corresponding, alternate interior, and exterior angles, to find unknown angle measures in a clear and structured manner.

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Solving Angle Measures in Parallel Lines Cut by Transversals

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  1. In the figure below, lines s and t are parallel and are cut by transversal wto form the angles shown. If the measure of 5 = 43°, what is the measure, in degrees, of 8?

  2. In the figure below, XY || JK and are cut by transversals XZ and YJ toform the angles shown.If XYJ = 46°and KJZ = 75°, what is the measure of ZJY?

  3. In the figure below, ST || QG and are intersected bytransversals TQ and TG as shown.What is the measure of TQH?

  4. In the figure below, XY ||WZ and are cut by transversals XV and YW .What is the measure of VWZ ?

  5. In this figure, lines j, k, and m intersect and form the angles as shown. If 3 = 40°and 5 = 35°, what is the measure of 4?

  6. In the figure below, MN || KL and are intersected by transversalsML and KN .What is the measure of XMN?

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