Question
Geometry Basics Unit Test
6 of 156 of 15 Items
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 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.
The measurement of angle upper N upper K upper I is 112 degrees.
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Answers
GPT-4o mini
To solve for the measurement of ∠NKI:
1. Carlos first constructs the angle bisector of ∠JKI, which measures 56 degrees. When he constructs ray KM, it divides ∠JKI into two equal parts:
\[
\text{Measurement of } ∠JKM = \text{Measurement of } ∠MKI = \frac{56 \text{ degrees}}{2} = 28 \text{ degrees}.
\]
2. Carlos then constructs the angle bisector of ∠MKI by constructing ray KN. Since he is bisecting ∠MKI, which is 28 degrees:
\[
\text{Measurement of } ∠NKI = \frac{28 \text{ degrees}}{2} = 14 \text{ degrees}.
\]
Therefore, the measurement of ∠NKI is **14 degrees**.
So the correct response is:
The measurement of ∠NKI is 14 degrees.
1. Carlos first constructs the angle bisector of ∠JKI, which measures 56 degrees. When he constructs ray KM, it divides ∠JKI into two equal parts:
\[
\text{Measurement of } ∠JKM = \text{Measurement of } ∠MKI = \frac{56 \text{ degrees}}{2} = 28 \text{ degrees}.
\]
2. Carlos then constructs the angle bisector of ∠MKI by constructing ray KN. Since he is bisecting ∠MKI, which is 28 degrees:
\[
\text{Measurement of } ∠NKI = \frac{28 \text{ degrees}}{2} = 14 \text{ degrees}.
\]
Therefore, the measurement of ∠NKI is **14 degrees**.
So the correct response is:
The measurement of ∠NKI is 14 degrees.