Question

The measure of one of the angles formed by two parallel lines and a transversal is 45°. Is it possible for the measure of any of the other seven angles to be equal to 55°? Explain.

Answer 1

Answer: No

Explanation:

Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.