Final answer:
To prove that angles LABD and LEBC are complementary, we use the given equations showing relationships between angles and properties of bisectors, concluding that their sum is 90 degrees.
Step-by-step explanation:
The question asks us to prove that angles LABD and LEBC are complementary given that BD bisects BC and the mathematical expressions provided. According to the given equations, if we assume that LABD equals LDBE, then to prove they are complementary, we need to show that their sum is 90 degrees. We have the following expressions:
Equation 7.74: A+B=C+D
Equation 7.69: Ce-BL +De+BL = FetikL
Substituted into Equation 7.65.
This substitution implies a relationship between the angles that could lead to the conclusion that the sum of LABD and LEBC is 90 degrees, thus proving they are complementary. Since BD bisects BC, we know that LDBE is equal to LEBC. From this information, if we consider the angle sum property and properties of bisectors, we can conclude that the angles in question are complementary.