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

The measurement of ∠NKI
∠
𝑁
𝐾
𝐼
is 14 degrees.
The measurement of angle upper N upper K upper I is 14 degrees.

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

The measurement of ∠NKI
∠
𝑁
𝐾
𝐼
is 28 degrees.
The measurement of angle upper N upper K upper I is 28 degrees.

Answer 1

To find the measurement of angle \( \angle NKI \), we start with the measurement of \( \angle JKI \), which is given as \( 56^\circ \).

1. Carlos first constructs the angle bisector ray \( KM \), which divides \( \angle JKI \) into two equal angles. Therefore:
\[
\angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ
\]

2. Next, Carlos constructs the angle bisector ray \( KN \) of \( \angle MKI \). Since \( \angle MKI \) is \( 28^\circ \), the angle bisector will divide this angle into two equal parts:
\[
\angle NKI = \frac{28^\circ}{2} = 14^\circ
\]

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

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