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Home > INT1 > Chapter 8 > Lesson 8.2.3 > Problem 8-122

8-122.

Use the relationships in the diagrams below to solve for , if possible. If it is not possible, state how you know. If it is possible, justify your solution by stating which geometric relationships you use.   

  1. Triangles with angles x + 8 degrees, 2 x + 3 degrees, and 3 x minus 2 degrees.

    The angles in a triangle sum to .
    So, .

  1. A vertical transversal cuts through 2 parallel lines. At the intersection of the top parallel line and the transversal, the angle, exterior, left is 6 x, minus 28 degrees.  At the intersection of the bottom parallel line and the transversal, the angle, exterior, right is 4 x, plus 18 degrees.

  1. An isosceles triangle where the base line is extended to the right outside of the triangle. A transversal parallel to the left side of the triangle passes through the right base vertex of the triangle. The angle between the two equal sides is labeled x. The angle between the extended side and the transversal is 56 degrees.

    How can you use the parallel lines to find an angle within the triangle?

    An isosceles triangle where the base line is extended to the right outside of the triangle. A transversal parallel to the left side of the triangle passes through the right base vertex of the triangle. The angle between the two equal sides is labeled x. The angle between the extended side and the transversal is 56 degrees. The angle between the triangle base and the transversal is 56 degrees.