Sam constructed the angle bisector of ∠ ABC by constructing BD−→− . Sam then constructed the angle bisector of ∠ DBC by constructing BE−→− . If the measurement of ∠ ABC is 54 degrees, what is the measurement of ∠ EBC?(1 point) Responses The measurement of ∠ EBC is 13.5 degrees. The measurement of angleEBC is 13.5 degrees. The measurement of ∠ EBC is 14 degrees. The measurement of angleEBC is 14 degrees. The measurement of ∠ EBC is 27 degrees. The measurement of angleEBC is 27 degrees. The measurement of ∠ EBC is 108 degrees.

Answer 1

To find the measurement of angle \( EBC \), we start with the given information about angle \( ABC \).

1. Measurement of angle \( ABC \): 54 degrees.

2. Construction of angle bisector \( BD \) of angle \( ABC \): The angle bisector divides the angle \( ABC \) into two equal angles: \[ \angle ABD = \angle DBC = \frac{54}{2} = 27 \text{ degrees} \]

3. Construction of angle bisector \( BE \) of angle \( DBC \): Now, we need to bisect angle \( DBC \): \[ \angle EBD = \angle EBC = \frac{27}{2} = 13.5 \text{ degrees} \]

Thus, the measurement of \( \angle EBC \) is \( 13.5 \) degrees.

The correct responses are:

• The measurement of ∠ EBC is 13.5 degrees.
• The measurement of angle EBC is 13.5 degrees.

Both options effectively say the same thing, with slight variations in wording. Either can be considered correct.