Carlos constructed the angle bisector of ∠JKI by constructing ray KM. Carlos then constructed the angle bisector of ∠MKI by constructing ray KN. If the measurement of ∠JKI is 56 degrees, what is the measurement of ∠NKI?(1 point)ResponsesThe measurement of ∠NKI is 14 degrees.The measurement of angle upper N upper K upper I is 14 degrees.The measurement of ∠NKI is 28 degrees.The measurement of angle upper N upper K upper I is 28 degrees.The measurement of ∠NKI is 112 degrees.The measurement of angle upper N upper K upper I is 112 degrees.The measurement of ∠NKI is 7 degrees.

Answer 1

To find the measurement of angle \( \angle NKI \), we first need to analyze the given angles and their relationships.

1. The measure of \( \angle JKI \) is given as 56 degrees.

2. Carlos constructs ray \( KM \) as the bisector of \( \angle JKI \). Therefore:

   \[ \angle JKM = \angle MKI = \frac{56}{2} = 28 \text{ degrees} \]

3. Next, Carlos constructs ray \( KN \) as the bisector of \( \angle MKI \). Since \( \angle MKI = 28 \) degrees, we find:

   \[ \angle NKI = \frac{28}{2} = 14 \text{ degrees} \]

Thus, the measurement of \( \angle NKI \) is 14 degrees.

The correct response is:

• The measurement of \( \angle NKI \) is 14 degrees.