Carlos constructed the angle bisector of ∠JKI

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.

1 answer

To solve for the measurement of angle \( \angle NKI \) given that \( \angle JKI \) measures 56 degrees, we can follow these steps:

  1. Since Carlos constructed ray \( KM \) as the angle bisector of \( \angle JKI \), the measure of each of the resulting angles \( \angle JKM \) and \( \angle MKI \) will be half of \( \angle JKI \): \[ \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ. \]

  2. Next, Carlos constructs ray \( KN \) as the angle bisector of \( \angle MKI \). Therefore, the measure of each of the angles created by \( KN \) will be half of \( \angle MKI \): \[ \angle NKI = \frac{28^\circ}{2} = 14^\circ. \]

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

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