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

Answer 1

To find the measurement of \( \angle NKI \), we need to go through the construction steps given the initial measurement of \( \angle JKI \).

1. The angle \( \angle JKI \) measures 56 degrees.
2. Carlos constructs ray \( KM \), which is the angle bisector of \( \angle JKI \). Therefore, \( \angle JKM \) and \( \angle MKI \) are each half of \( \angle JKI \). \[ \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ \]
3. Carlos then constructs ray \( KN \), which is the angle bisector of \( \angle MKI \). Since \( \angle MKI = 28^\circ \), the angles \( \angle MKN \) and \( \angle NKI \) will also be half of \( \angle MKI \). \[ \angle MKN = \angle NKI = \frac{28^\circ}{2} = 14^\circ \]

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

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