Carlos constructed the angle bisector of ∠JKI

Question

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

Answer 1

To find the measurement of ∠NKI, we need to follow the details provided about the angles and their bisectors.

1. The measurement of ∠JKI is given as 56 degrees.
2. Carlos constructs the angle bisector KM of ∠JKI. Thus, each of the two angles created (∠JKM and ∠MKI) will be half of 56 degrees: \[ \text{Measurement of } ∠JKM = \text{Measurement of } ∠MKI = \frac{56}{2} = 28 \text{ degrees.} \]
3. Next, Carlos constructs the angle bisector KN of ∠MKI. Since ∠MKI measures 28 degrees, the angle bisector will split it into two equal angles: \[ \text{Measurement of } ∠NKI = \frac{28}{2} = 14 \text{ degrees.} \]

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

The measurement of ∠NKI is 14 degrees.