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Home > INT1 > Chapter 1 > Lesson 1.2.1 > Problem 1-42

1-42.

Recall what you learned about angle relationships in previous courses. (See the Math Notes box in this lesson if you need a reminder.) Determine the measures of the labeled angles. The double arrowheads indicate that the pair of lines is parallel.

All three of these can be solved using multiple techniques related to parallel lines.

  1. 2 horizontal parallel lines, p, & q, are crossed by a transversal line, m, with angles labeled as follows: Intersection of m, and, p: exterior right, a, & interior left, b. Intersection of m, and, q: interior left, c, interior right, 123 degrees.

    : Corresponding angle with , so  .
    : and are vertical angles, so they have equal measures. Therefore, .
    : and form a pair of supplementary angles, so .

  1. Decreasing Transversal line, m, crosses two increasing parallel lines, p, and, q, Angles are labeled as follows: Intersection of m, and, p: exterior bottom, d, and interior top, e, Intersection of m, and, q, interior bottom, f, exterior bottom, 82 degrees.

    and form a pair of supplementary angles. How are and related?

  1. Vertical Transversal line, m, crosses 2 parallel lines, p, and, q, with Angles labeled as follows: Intersection of m, and, p: interior right, 75 degrees. Intersection of m, and, q: interior left, g and exterior right, h.

    Since there are parallel lines, look for relationships between pairs of angles such as alternate interior, corresponding, or same-side interior.

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