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How Do You Find Missing Angles in a Transversal Diagram?

If l and m are parallel, find the values for all the angles in the diagram below

Summary

  1. A line that intersects two parallel lines, like line P, is called a transversal
  2. Vertical angles, like our angle and angle 5, are always congruent
  3. Corresponding angles, like our angle and angle 4, are always congruent
  4. Alternate exterior angles, like our angle and angle 1, are always congruent

Notes

    1. Parallel lines are lines that do not intersect.
    2. An angle is formed by two rays connected by a common endpoint.
    3. A transversal is a line that intersects two or more parallel lines.
    1. Acute angles are angles that measure less than 90°
    1. Acute angles are angles that measure less than 90°
    2. Vertical angles are angles which are opposite each other when two lines cross.
    3. When angles are congruent, it means they have the same measurement.
    4. Our angle and angle 5 are vertical angles, so they are congruent
    1. Acute angles are angles that measure less than 90°
    2. When angles are congruent, it means they have the same measurement.
    3. Corresponding angles are in the same location relative to the transversal
    4. Our angle and angle 4 are corresponding angles, so they are congruent
    1. Acute angles are angles that measure less than 90°
    2. When angles are congruent, it means they have the same measurement.
    3. The pairs of angles outside the parallel lines on opposite sides of a transversal line are alternate exterior angles
    4. Our angle and angle 1 are alternate exterior angles, so they are congruent
    1. Obtuse angles are angles that measure more than 90° but less than 180°
    2. Angles are adjacent if they have a common side and a common vertex.
    1. Obtuse angles are angles that measure more than 90° but less than 180°
    2. Angles are adjacent if they have a common side and a common vertex.
    3. Angle 6 and our angle are adjacent and form a straight line, so they are supplementary
    1. Acute angles are angles that measure less than 90°
    2. Obtuse angles are angles that measure more than 90° but less than 180°
    3. Angles are adjacent if they have a common side and a common vertex.
    4. In our diagram, each obtuse angle is supplementary to one of the acute angles
    5. So since all the acute angles are equal, all the obtuse angles are equal as well