Carlos constructed the angle bisector of ∠JKI

Question

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 which answer is 100 percent correct

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 7 degrees.
The measurement of angle upper N upper K upper I is 7 degrees.

The measurement of ∠NKI
is 112 degrees.

Answer 1

To find the measurement of ∠NKI, we first need to understand the construction of the angle bisectors.

1. Measurement of ∠JKI is given as 56 degrees.

   • Since KM is the angle bisector of ∠JKI, then: \[ \angle JKQ = \angle MKI = \frac{56}{2} = 28 \text{ degrees} \] (where Q is a point on ray KM).

2. Next, we construct the angle bisector of ∠MKI (which is now known to be 28 degrees) with ray KN. Thus: \[ \angle MKI = \angle NKI = \frac{28}{2} = 14 \text{ degrees} \]

Now, we can conclude: The measurement of ∠NKI is 14 degrees.

Thus, the correct response is: "The measurement of ∠NKI is 14 degrees."