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) the measurement of ∠nki is 28 degrees. the measurement of ∠nki is 7 degrees. the measurement of ∠nki is 14 degrees. the measurement of ∠nki is 112 degrees.

Explanation:

Step1: Find measure of ∠MKI

Since ray $KM$ is the angle - bisector of $\angle{JKI}$ and $\angle{JKI}=56^{\circ}$, then $\angle{MKI}=\frac{1}{2}\angle{JKI}$.
$\angle{MKI}=\frac{1}{2}\times56^{\circ}=28^{\circ}$

Step2: Find measure of ∠NKI

Since ray $KN$ is the angle - bisector of $\angle{MKI}$, then $\angle{NKI}=\frac{1}{2}\angle{MKI}$.
$\angle{NKI}=\frac{1}{2}\times28^{\circ}=14^{\circ}$

Answer:

The measurement of $\angle{NKI}$ is 14 degrees.