Question

In the triangle ABC, where ∠ABD is supplementary to ∠EDB, BC bisects ∠ABD, and DC bisects ∠BDE, and ∠CBD is complementary to ∠BDC, what is the relationship between these angles?

a) ∠CBD≅∠BDC
b) ∠CBD≅∠ABD
c) ∠BDE≅∠ABD
d) ∠ABD≅∠EDB

Answer 1

Using properties of angles, we conclude that ∠CBD ≅ ∠BDC as they are both 45 degrees, resulting from being complementary angles that are bisected.

Step-by-step explanation:

To determine the relationship between the angles in triangle ABC, we must apply our knowledge of angle properties. We are given that ∠ABD is supplementary to ∠EDB, meaning that their sum is 180 degrees. This implies that if one angle is known, the other can be calculated by subtracting from 180 degrees. Furthermore, we know that BC bisects ∠ABD and DC bisect ∠BDE, implying that each angle is divided into two equal parts. Lastly, ∠CBD is complementary to ∠BDC, meaning their sum is 90 degrees. Since these angles are also bisected, we can conclude that ∠CBD ≅ ∠BDC, each being half of 90 degrees, which is 45 degrees.