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 112 degrees.
The measurement of angle upper N upper K upper I is 112 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 14 degrees.
The measurement of angle upper N upper K upper I is 14 degrees.

The measurement of ∠NKI
is 7 degrees.

Answer 1

To find the measurement of angle \( \angle NKI \), we can proceed as follows:

1. First, Carlos constructs the angle bisector \( KM \) of angle \( \angle JKI \), which measures \( 56^\circ \).

   • This means that \( \angle JKM \) and \( \angle MKI \) each measure half of \( 56^\circ \).
   • Therefore, \( \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ \).

2. Next, Carlos constructs the angle bisector \( KN \) of angle \( \angle MKI \).

   • The measurement of \( \angle MKI \) is \( 28^\circ \), so the angle bisector \( KN \) creates two equal angles: \( \angle NKM \) and \( \angle NKI \).
   • Thus, \( \angle NKM = \angle NKI = \frac{28^\circ}{2} = 14^\circ \).

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

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