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 determine the measurement of \( \angle NKI \), let's follow the steps of the bisector constructions.

  1. Carlos constructs the angle bisector of \( \angle JKI \) (which measures 56 degrees) and creates ray \( KM \). This means that \( \angle JKM \) and \( \angle MKI \) are each half of \( \angle JKI \): \[ \angle JKM = \angle MKI = \frac{56}{2} = 28 \text{ degrees} \]

  2. Next, Carlos constructs the angle bisector of \( \angle MKI \) by constructing ray \( KN \), which divides \( \angle MKI \) into two equal angles. Therefore, each angle will measure: \[ \angle MKN = \angle NKI = \frac{28}{2} = 14 \text{ degrees} \]

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

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