for two angles ABC and DBC the measure of ABC was 30 degrees and DBC is its complement. ray BE is the angle bisector of ABD. consider each angle. does the angle have a measure of 45 degrees? select yes or no for DBC ABE DBE

To determine whether each angle has a measure of 45 degrees, let's break down the information given:

1. Angle ABC: The measure of angle ABC is given as 30 degrees.

2. Angle DBC: It is mentioned that DBC is the complement of ABC. In other words, the sum of the measures of angle ABC and angle DBC is equal to 90 degrees. Since ABC is 30 degrees, DBC must be 90 - 30 = 60 degrees.

Now, let's consider each angle:

1. DBC: The measure of angle DBC is 60 degrees, not 45 degrees. Therefore, the answer is "No."

2. ABE: Ray BE is the angle bisector of ABD. An angle bisector divides an angle into two congruent angles. Since angle ABD is divided into two congruent angles, each of them would have a measure of (1/2) * 30 = 15 degrees. Therefore, the measure of angle ABE is 15 degrees, not 45 degrees. Again, the answer is "No."

3. DBE: Angle DBE is formed by the intersection of ray BE and ray BD. Since angle ABD is bisected by ray BE, angle DBE is one of the two congruent angles formed by the bisector. Therefore, just like angle ABE, the measure of angle DBE is also 15 degrees, not 45 degrees. The answer remains "No."

So, the answer is "No" for all three angles: DBC, ABE, and DBE.

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