Final answer:
To prove ∠3 and ∠4 are complementary, it is assumed they form a triangle with ∠1 and ∠2, whose sum is 180 degrees. Since ∠1 and ∠2 are complementary (sum of 90 degrees), ∠3 and ∠4 must also sum up to 90 degrees, proving they are complementary.
Step-by-step explanation:
To prove that ∠3 and ∠4 are complementary angles given that ∠1 and ∠2 are complementary, we first need to recall that complementary angles are two angles whose sum is 90 degrees. The question seems to be indirectly stating that ∠3 and ∠4 are related to ∠1 and ∠2 such that they form a triangle, given the mention of the sum of angles in a triangle being 180 degrees. If ∠1 and ∠2 are complementary, their sum is 90 degrees. Now, if ∠3 is adjacent to ∠1 and ∠4 is adjacent to ∠2 within a triangle, then the sum of ∠3 and ∠4 must be the third angle of the triangle, making it also 90 degrees to account for the triangle's total angle sum of 180 degrees. Therefore, ∠3 and ∠4 are complementary by definition.