1. The problem asks which pair of angles has a sum of 180° given two parallel lines PQ and RS cut by a transversal. 2. When two parallel lines are cut by a transversal, pairs of angles that are supplementary (sum to 180°) include consecutive interior angles. 3. Consecutive interior angles lie on the same side of the transversal and between the two lines. 4. From the figure description, angles 4 and 5 are consecutive interior angles, so their sum is 180°. 5. Therefore, the correct answer is C: ∠4 and ∠5. 6. The second question asks about the application of the Pythagorean theorem. 7. The Pythagorean theorem applies only to right-angled triangles, where one angle is exactly 90°. 8. It states that in a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relation is $$a^2 + b^2 = c^2$$. 9. This theorem is not applicable to triangles without a right angle. Final answers: - For 1.6: Pair of angles with sum 180° is ∠4 and ∠5. - For 1.7: Pythagorean theorem applies only to right-angled triangles.