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Solving Angles within Parallel Lines: Understanding Supplementary Angles

This problem explores the relationships between angles formed when a line is drawn parallel to two others. By establishing a new line through point A parallel to lines BC and ED, we create two new angles, x and y. Given that y measures 90° due to the formation of a rectangle, we can derive the measure of angle x using the property of supplementary angles: x + 130° = 180°. This leads to the conclusion that angle x equals 50°, showcasing the practical application of geometric principles in angle relationships.

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Solving Angles within Parallel Lines: Understanding Supplementary Angles

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  1. Problem 1 Objective 6

  2. 130°

  3. 130°

  4. To solve, draw a line through A parallel to BC and ED. 130°

  5. Now we can label our two new angles x and y. 130° x y

  6. We know that y = 90 because drawing our new line created a rectangle. 130° x y

  7. We know x + 130 = 180 because Same Side Interior Angles are supplementary. 130° 180° x y

  8. -130 = -130 x + 130 = 50 x + 130 = 180

  9. 130° x y

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