Question

Given 1- BC is parallel to DE

Given 2- Angle ABC and angle AED are complementary.
Prove that angles ABC and ACB are complementary

Answer 1

To prove that angles ABC and ACB are complementary, we can use the given information. Given 1 states that BC is parallel to DE. Given 2 states that angle ABC and angle AED are complementary.

Step-by-step explanation:

To prove that angles ABC and ACB are complementary, we can use the given information.

Given 1 states that BC is parallel to DE. This means that angles ABC and BDE are alternate interior angles and are congruent. Therefore, angle ABC is congruent to angle BDE.

Given 2 states that angle ABC and angle AED are complementary. This means that the sum of angle ABC and angle AED is 90 degrees. Since angle ABC is congruent to angle BDE, we can substitute congruent angles and conclude that the sum of angle BDE and angle AED is 90 degrees. Therefore, angle ACB and angle AED are also complementary.