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) Responses The measurement of ∠NKI is 7 degrees. The measurement of angle upper N upper K upper I is 7 degrees. The 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.

Answer 1

To find the measurement of angle \( \angle NKI \), we start with the measurements given.

1. The measurement of \( \angle JKI \) is \( 56^\circ \).
2. Carlos constructs the angle bisector of \( \angle JKI \), which means \( \angle JKM \) and \( \angle MKI \) are both half of \( \angle JKI \).

Calculating the measures of these angles: \[ \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ \]

3. Next, Carlos constructs the angle bisector of \( \angle MKI \). Therefore, \( \angle NKI \) is half of \( \angle MKI \).

Calculating \( \angle NKI \): \[ \angle NKI = \frac{\angle MKI}{2} = \frac{28^\circ}{2} = 14^\circ \]

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

Therefore, the correct response is: The measurement of angle \( NKI \) is 14 degrees.