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)

Question

Responses

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 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 112 degrees.

Answer 1

To determine the measurement of angle \( \angle NKI \), we can follow these steps based on the geometry of the situation:

1. Understanding the angle bisectors:

   • Carlos first bisected \( \angle JKI \) which measures 56 degrees. Therefore, the two angles formed are: \[ \angle JKD = \angle DKY = \frac{56^\circ}{2} = 28^\circ \]
   • Now we have: \[ \angle JKM = 28^\circ \]

2. Constructing the second angle bisector:

   • Carlos then bisected \( \angle MKI \). The angle \( \angle MKI \) can now be calculated. Since \( M \) is on the bisector of \( \angle JKI \), the angle \( \angle MKI \) measures: \[ \angle MKI = 180^\circ - \angle JKM = 180^\circ - 28^\circ = 152^\circ \]

3. Finding the measurement of angle \( \angle NKI \):

   • Carlos then bisected the angle \( \angle MKI \) as well: \[ \angle NKI = \frac{152^\circ}{2} = 76^\circ \]

Now we need to correct our calculation for \( \angle NKI \):

• From \( \angle JKI = 56^\circ \), we can confirm that: \[ \angle NKI = 28^\circ \]

Therefore, the measurement of \( \angle NKI \) is \( 28^\circ \).

So, the correct response is:

• The measurement of \( \angle NKI \) is 28 degrees.