Thank you for visiting What is the measure of angle AEB Enter your answer as a whole number. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
The value of angle [tex]\(AEB\)[/tex] is 66 (as a whole number).
find the measure of angle [tex]\(AEB\)[/tex] step by step using the information given in the image.
1. Given Information:
- We have a circle with points A, B, C, D, and E on its circumference.
- Arc AB measures [tex]\(57^\circ\)[/tex], and Arc CD measures [tex]\(75^\circ\)[/tex].
2. Theorem for Intersecting Chords:
- The measure of the angle formed by two chords that intersect inside the circle is half the sum of the measures of the intercepted arcs.
- In other words:
[tex]\[ \text{Angle AEB} = \frac{1}{2}(\text{Arc AB} + \text{Arc CD}) \][/tex]
3. Calculating the Sum of Arcs:
- Sum of the intercepted arcs:
[tex]\[ \text{Arc AB} + \text{Arc CD} = 57^\circ + 75^\circ = 132^\circ \][/tex]
- Half of this sum:
[tex]\[ \frac{1}{2} \cdot 132^\circ = 66^\circ \][/tex]
4. Final Answer:
- The measure of angle [tex]\(AEB\) is \(66^\circ\)[/tex].
Therefore, the value of angle [tex]\(AEB\)[/tex] is 66 (as a whole number).
Thank you for reading the article What is the measure of angle AEB Enter your answer as a whole number. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
Rewritten by : Jeany
