Question

Carlos constructed the angle bisector of ∠JKI
∠
J
K
I
by constructing ray KM
K
M
. Carlos then constructed the angle bisector of ∠MKI
∠
M
K
I
by constructing ray KN
K
N
. If the measurement of ∠JKI
∠
J
K
I
is 56 degrees, what is the measurement of ∠NKI
∠
N
K
I
?(1 point)
Responses

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.
The measurement of angle upper N upper K upper I is 7 degrees.

The measurement of ∠NKI
is 14 degrees.

Answer 1

To find the measurement of ∠NKI, we can follow the steps of the angle bisector constructions made by Carlos.

1. **Understanding the angle:**
- The measurement of ∠JKI is given as 56 degrees.

2. **First angle bisector (ray KM):**
- Ray KM is the angle bisector of ∠JKI, which means it divides ∠JKI into two equal parts.
- Therefore, ∠JKM = ∠MKI = 56 degrees / 2 = 28 degrees.

3. **Second angle bisector (ray KN):**
- Next, ray KN is the angle bisector of ∠MKI which we found to be 28 degrees.
- Thus, it divides ∠MKI into two equal parts.
- Therefore, ∠NKI = ∠MKN = 28 degrees / 2 = 14 degrees.

Thus, the measurement of ∠NKI is **14 degrees**.

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