Carlos constructed the angle bisector of ∠JKI ∠ 𝐽 𝐾 𝐼 by constructing ray KM 𝐾 𝑀 . Carlos then constructed the angle bisector of ∠MKI ∠ 𝑀 𝐾 𝐼 by constructing ray KN 𝐾 𝑁 . If the measurement of ∠JKI ∠ 𝐽 𝐾 𝐼 is 56 degrees, what is the measurement of ∠NKI ∠ 𝑁 𝐾 𝐼 ?(1 point) Responses The measurement of ∠NKI ∠ 𝑁 𝐾 𝐼 is 7 degrees. The measurement of angle upper N upper K upper I is 7 degrees. The measurement of ∠NKI ∠ 𝑁 𝐾 𝐼 is 112 degrees. The measurement of angle upper N upper K upper I is 112 degrees. The measurement of ∠NKI ∠ 𝑁 𝐾 𝐼 is 14 degrees. The measurement of angle upper N upper K upper I is 14 degrees. The measurement of ∠NKI ∠ 𝑁 𝐾 𝐼 is 28 degrees.

Question

GPT-4o mini · Answer

To find the measurement of angle $ \angle NKI $, we first need to understand how angles are bisected through the construction. 1. We know that $ \angle JKI $ measures 56 degrees. 2. Carlos constructs the angle bisector $ KM $ of $ \angle JKI $, which means that $ \angle JKM $ and $ \angle MKI $ are both half of $ \angle JKI $. Therefore, each of those angles measures: $$ \angle JKM = \angle MKI = \frac{56}{2} = 28 \text{ degrees} $$ 3. Next, he constructs the angle bisector $ KN $ of $ \angle MKI $. $ \angle MKI $ measures 28 degrees, so when he bisects it, we have: $$ \angle NKI = \angle MKI / 2 = \frac{28}{2} = 14 \text{ degrees} $$ Thus, the measurement of $ \angle NKI $ is **14 degrees**. The correct response is: "The measurement of angle $ NKI $ is 14 degrees."