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 112°. the measurement of ∠nki is 7°. the measurement of ∠nki is 14°. the measurement of ∠nki is 28°.

Explanation:

Step1: Find measure of ∠MKI

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

Step2: Find measure of ∠NKI

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

Answer:

The measurement of ∠NKI is 14°.