The ratio of the same side interior angles of two parallel lines is 33:3. Find the measures of all eight angles formed by the parallel lines and transversal.

9514 1404 393

  all 4 acute angles: 15 degrees

  all 4 obtuse angles: 165 degrees

Step-by-step explanation:

The sum of same-side interior angles between parallel lines is 180°. The smallest of them will be 3/(33+3) = 1/12 of 180°, or 15°. The largest will be 180° -15° = (33/3)(15°) = 165°. All remaining angles are congruent to one or the other of these.

  All four acute angles are 15°; all four obtuse angles are 165°.