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)

Question

Responses

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 112 degrees.
The measurement of angle upper N upper K upper I is 112 degrees.

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 28 degrees.

Answer 1

To find the measurement of ∠NKI, we start with the information given:

1. The measurement of ∠JKI is 56 degrees.
2. Carlos constructs ray KM, which is the angle bisector of ∠JKI, so ∠JKM and ∠MKI will each be half of ∠JKI.

Calculating that: \[ \angle JKM = \angle MKI = \frac{56°}{2} = 28° \]

3. Next, Carlos constructs the angle bisector of ∠MKI by constructing ray KN. Because KM is the bisector of ∠JKI, we now look specifically at ∠MKI, which is 28 degrees. Therefore: \[ \angle MKN = \angle NKI = \frac{28°}{2} = 14° \]

So, the measurement of ∠NKI is 14 degrees.

The correct response is: The measurement of ∠NKI is 14 degrees.