Question

Given that B is the midpoint of EF, CA is the perpendicular bisector of EF, DB bisects angle EBC, and EF = 11.8 units, what is the measure of angle DBE, and what is the length of BF?

A) DBE = 45 degrees, BF = 5.9 units
B) DBE = 90 degrees, BF = 11.8 units
C) DBE = 30 degrees, BF = 5.9 units
D) DBE = 60 degrees, BF = 11.8 units

Answer 1

The measure of angle DBE is 45 degrees, and the length of BF is 5.9 units. Hence the correct answer is option A

Step-by-step explanation:

Given that B is the midpoint of EF, CA is the perpendicular bisector of EF, and DB bisects angle EBC, we can use the properties of perpendicular bisectors and angle bisectors to find the measure of angle DBE and the length of BF.

Since B is the midpoint of EF, BE is equal to BF. Since CA is the perpendicular bisector of EF, CE is also equal to BF. Therefore, BE = CE = BF = 11.8/2 = 5.9 units.

Since DB bisects angle EBC, angle DBE is half of angle EBC. Since EB = BF, angles EBF and DBE are congruent. Therefore, angle DBE is half of angle EBF. Since angle EBF is a right angle, angle DBE is 90 degrees / 2 = 45 degrees.

Hence the correct answer is option A