Answer :

Two parallel lines cut by a transversal create corresponding, alternate interior, alternate exterior, and consecutive interior angles. These angles can be used to find unknown measurements by applying their properties.

When two parallel lines are cut by a transversal, several angle relationships are formed. These relationships are useful for finding unknown measurements. Here are the main types of angles formed:

  • Corresponding Angles: Angles that are in the same relative position at each intersection where the transversal crosses the parallel lines. These angles are equal. For example, if angle 1 and angle 2 are corresponding angles, then angle 1 = angle 2.
  • Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the parallel lines. These angles are also equal. For example, if angle 3 and angle 4 are alternate interior angles, then angle 3 = angle 4.
  • Alternate Exterior Angles: Angles that are on opposite sides of the transversal and outside the parallel lines. These angles are equal as well. For example, if angle 5 and angle 6 are alternate exterior angles, then angle 5 = angle 6.
  • Consecutive Interior Angles: Also known as same-side interior angles, these angles are on the same side of the transversal and inside the parallel lines. These angles are supplementary, meaning their measures add up to 180 degrees.

For example, if angle 7 and angle 8 are consecutive interior angles, then

angle 7 + angle 8 = 180 degrees.

To solve for the measures of angles formed by two parallel lines and a transversal, follow these steps:

  • Identify the angle relationships: Determine which angles are corresponding, alternate interior, alternate exterior, or consecutive interior.
  • Use the relationships: Apply the properties like equality of corresponding, alternate interior, and alternate exterior angles, or the supplementary nature of consecutive interior angles.
  • Set up equations: Use the properties to set up equations and solve for the unknown angles.

For example, if one of the alternate interior angles is known to be 70 degrees, the other alternate interior angle will also be 70 degrees.

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Rewritten by : Barada