Carlos constructed the angle bisector ot ∠JKI by constructing ⟶KM. Carlos then constructed the angle bisector of ∠MKI bu constructing ⟶KN. If the measurement of ∠JKI is 56°, what is the measurement of ∠NKI?

Question

Hint: draw a picture
• 7°
• 14°
• 28°
• 112°

Answer 1

To find the measurement of \( \angle NKI \), we begin with the given information about the angles and the construction of angle bisectors.

1. Carlos constructed the angle bisector of \( \angle JKI \), which has a measure of 56°. This means that \( \angle JKM \) (the angle on one side of the bisector) and \( \angle MKI \) (the angle on the other side of the bisector) are both equal. Therefore:

   \[ \angle JKM = \angle MKI = \frac{56°}{2} = 28° \]

2. Next, Carlos constructed the angle bisector of \( \angle MKI \). Since we found that \( \angle MKI \) is 28°, bisecting it gives:

   \[ \angle NKI = \frac{28°}{2} = 14° \]

Hence, the measurement of \( \angle NKI \) is \( 14° \).

So the correct answer is 14°.