Question

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)
Responses

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

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.

Answer 1

To find the measurement of ∠NKI, we start by analyzing the situation step by step.

1. We know the measurement of ∠JKI is 56 degrees.
2. Since Carlos bisects ∠JKI using ray KM, we find that ∠JMK is half of ∠JKI: \[ ∠JMK = \frac{56}{2} = 28 \text{ degrees} \]
3. Next, Carlos constructs the angle bisector of ∠MKI using ray KN. The angle ∠MKI is composed of ∠JMK and ∠JKI. Therefore, we first find the measurement of ∠MKI: \[ ∠MKI = ∠JMK + ∠JKI = 28 + 28 = 56 \text{ degrees} \]
4. Now, we can bisect ∠MKI. Since ∠MKI is 56 degrees, we find that ∠NKI, which is one of the resulting angles from the bisection, is: \[ ∠NKI = \frac{56}{2} = 28 \text{ degrees} \]

Thus, the measurement of ∠NKI is 28 degrees.

The correct response is: The measurement of ∠NKI is 28 degrees.