Question
Carlos constructed the angle bisector of ∠JKI by constructing ray K M. Carlos then constructed the angle bisector of ∠MKI by constructing ray K N. If the measurement of ∠JKI is 56 degrees, what is the measurement of ∠NKI?
The measurement of ∠NKI is 28 degrees.
The measurement of ∠NKI is 7 degrees.
The measurement of ∠NKI is 14 degrees.
The measurement of ∠NKI is 112 degrees.
The measurement of ∠NKI is 28 degrees.
The measurement of ∠NKI is 7 degrees.
The measurement of ∠NKI is 14 degrees.
The measurement of ∠NKI is 112 degrees.
Answers
Answered by
GPT-4o mini
To find the measurement of \(\angle NKI\), we first need to analyze the angle bisector constructions provided by Carlos.
1. Carlos constructs the angle bisector of \(\angle JKI\) which measures 56 degrees. By bisecting this angle with ray \(KM\), we have:
\[
\angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ
\]
2. Next, Carlos constructs the angle bisector of \(\angle MKI\) with ray \(KN\). Since \(\angle MKI\) measures 28 degrees, we apply the angle bisector concept again:
\[
\angle NKI = \frac{\angle MKI}{2} = \frac{28^\circ}{2} = 14^\circ
\]
Thus, the measurement of \(\angle NKI\) is \( \boxed{14} \) degrees.
1. Carlos constructs the angle bisector of \(\angle JKI\) which measures 56 degrees. By bisecting this angle with ray \(KM\), we have:
\[
\angle JKM = \angle MKI = \frac{56^\circ}{2} = 28^\circ
\]
2. Next, Carlos constructs the angle bisector of \(\angle MKI\) with ray \(KN\). Since \(\angle MKI\) measures 28 degrees, we apply the angle bisector concept again:
\[
\angle NKI = \frac{\angle MKI}{2} = \frac{28^\circ}{2} = 14^\circ
\]
Thus, the measurement of \(\angle NKI\) is \( \boxed{14} \) degrees.