Sure, let's go through the process of determining the measure of an inscribed angle that intercepts an arc of 114° in a circle.
1. Understand the Relationship:
- An inscribed angle in a circle is an angle whose vertex is on the circle, and its sides contain chords of the circle.
- An important property of an inscribed angle is that it measures half of the measure of the intercepted arc.
2. Given Data:
- The intercepted arc measure is given as 114°.
3. Apply the Inscribed Angle Theorem:
- The inscribed angle measures half the intercepted arc.
- To find the measure of the inscribed angle, divide the intercepted arc measure by 2.
4. Perform the Calculation:
- [tex]\( \text{Inscribed Angle Measure} = \frac{\text{Intercepted Arc Measure}}{2} = \frac{114°}{2} = 57° \)[/tex]
So, the measure of the inscribed angle that intercepts an arc of 114° is 57°.
Therefore, the correct answer is:
[tex]\[ \boxed{57°} \][/tex]
