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)ResponsesThe 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.The measurement of angle upper N upper K upper I is 28 degrees.The measurement of ∠NKI is 7 degrees.

Question

GPT-4o mini · Answer

To find the measurement of angle $ NKI $, we can follow these steps based on the information provided: 1. The measure of angle $ JKI $ is given as $ 56^\circ $. 2. Carlos first constructs ray $ KM $, which bisects angle $ JKI $. This means that the measure of angle $ MKI $ is half of $ JKI $. $$ \text{Measure of } \angle MKI = \frac{1}{2} \times 56^\circ = 28^\circ $$ 3. Next, Carlos constructs ray $ KN $, which bisects angle $ MKI $. Therefore, the measure of angle $ NKI $ is half of $ MKI $. $$ \text{Measure of } \angle NKI = \frac{1}{2} \times 28^\circ = 14^\circ $$ Thus, the measurement of angle $ NKI $ is $ 14^\circ $. The correct response is: **The measurement of angle $ NKI $ is 14 degrees.**