Question
Carlos constructed the angle bisector of ∠JKI%0D%0A∠%0D%0A𝐽%0D%0A𝐾%0D%0A𝐼%0D%0A by constructing ray KM%0D%0A𝐾%0D%0A𝑀%0D%0A. Carlos then constructed the angle bisector of ∠MKI%0D%0A∠%0D%0A𝑀%0D%0A𝐾%0D%0A𝐼%0D%0A by constructing ray KN%0D%0A𝐾%0D%0A𝑁%0D%0A. If the measurement of ∠JKI%0D%0A∠%0D%0A𝐽%0D%0A𝐾%0D%0A𝐼%0D%0A is 56 degrees, what is the measurement of ∠NKI%0D%0A∠%0D%0A𝑁%0D%0A𝐾%0D%0A𝐼%0D%0A?(1 point)%0D%0AResponses%0D%0A%0D%0AThe measurement of ∠NKI%0D%0A∠%0D%0A𝑁%0D%0A𝐾%0D%0A𝐼%0D%0A is 7 degrees.%0D%0AThe measurement of angle upper N upper K upper I is 7 degrees.%0D%0A%0D%0AThe measurement of ∠NKI%0D%0A∠%0D%0A𝑁%0D%0A𝐾%0D%0A𝐼%0D%0A is 28 degrees.%0D%0AThe measurement of angle upper N upper K upper I is 28 degrees.%0D%0A%0D%0AThe measurement of ∠NKI%0D%0A∠%0D%0A𝑁%0D%0A𝐾%0D%0A𝐼%0D%0A is 14 degrees.%0D%0AThe measurement of angle upper N upper K upper I is 14 degrees.%0D%0A%0D%0AThe measurement of ∠NKI%0D%0A∠%0D%0A𝑁%0D%0A𝐾%0D%0A𝐼%0D%0A is 112 degrees.
Answers
Answered by
GPT-4o mini
To solve for the measurement of ∠NKI, we start by analyzing how Carlos constructed the angle bisectors.
1. The initial angle ∠JKI measures 56 degrees. When Carlos constructs ray KM as the angle bisector of ∠JKI, this means that ∠JKM and ∠MKI are both equal to half of ∠JKI.
- \( \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ \)
2. Next, Carlos constructs the angle bisector of ∠MKI by constructing ray KN. This means that ∠MKL and ∠NKI are equal to half of ∠MKI.
- \( \angle MKI = 28^\circ \)
- So, \( \angle NKI = \angle MKL = \frac{28^\circ}{2} = 14^\circ \)
Thus, the measurement of ∠NKI is **14 degrees**.
Therefore, the correct response is:
**The measurement of ∠NKI is 14 degrees.**
1. The initial angle ∠JKI measures 56 degrees. When Carlos constructs ray KM as the angle bisector of ∠JKI, this means that ∠JKM and ∠MKI are both equal to half of ∠JKI.
- \( \angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ \)
2. Next, Carlos constructs the angle bisector of ∠MKI by constructing ray KN. This means that ∠MKL and ∠NKI are equal to half of ∠MKI.
- \( \angle MKI = 28^\circ \)
- So, \( \angle NKI = \angle MKL = \frac{28^\circ}{2} = 14^\circ \)
Thus, the measurement of ∠NKI is **14 degrees**.
Therefore, the correct response is:
**The measurement of ∠NKI is 14 degrees.**