Question

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.

Answer 1

To find the measurement of angle $\mathrm{\angle }NKI$, we start with the measurements given.

1. The measurement of $\mathrm{\angle }JKI$ is ${56}^{\circ }$.
2. Carlos constructs the angle bisector of $\mathrm{\angle }JKI$, which means $\mathrm{\angle }JKM$ and $\mathrm{\angle }MKI$ are both half of $\mathrm{\angle }JKI$.

Calculating the measures of these angles: $$\mathrm{\angle }JKM=\mathrm{\angle }MKI=\frac{{56}^{\circ }}{2}={28}^{\circ }$$

3. Next, Carlos constructs the angle bisector of $\mathrm{\angle }MKI$. Therefore, $\mathrm{\angle }NKI$ is half of $\mathrm{\angle }MKI$.

Calculating $\mathrm{\angle }NKI$: $$\mathrm{\angle }NKI=\frac{\mathrm{\angle }MKI}{2}=\frac{{28}^{\circ }}{2}={14}^{\circ }$$

Thus, the measurement of $\mathrm{\angle }NKI$ is ${14}^{\circ }$.

Therefore, the correct response is: The measurement of angle $NKI$ is 14 degrees.