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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 112 degrees. The measurement of angle upper N upper K upper I is 112 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 14 degrees.

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To solve this problem, let's go through the construction step by step.

  1. Carlos constructed the angle bisector of ∠JKI (which measures 56 degrees) creating ray KM.

    • Since KM is the angle bisector, it divides ∠JKI into two equal parts.
    • Therefore, ∠JKM = ∠MKI = 56 degrees / 2 = 28 degrees.

  2. Next, Carlos constructed the angle bisector of ∠MKI by constructing ray KN.

    • We already know that ∠MKI = 28 degrees, so ray KN will also bisect this angle.
    • Thus, ∠MKJ = ∠NKI = 28 degrees / 2 = 14 degrees.

Now, to find the measurement of ∠NKI, we do the following:

  • Since we have established that ∠MKI = 28 degrees and ray KN bisects it: \[ \text{The measurement of } \angle NKI = \frac{\angle MKI}{2} = \frac{28^\circ}{2} = 14^\circ \]

Therefore, the measurement of ∠NKI is 14 degrees.