Geometry Basics Unit Test

Question

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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Answer 1

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.