Math Problem Statement
Solution
The problem involves finding the angle in a circle with its center at , where the angle at the center is given as .
Step-by-Step Solution:
-
Understanding Circle Geometry: The angle lies on the circumference of the circle, and it subtends the same arc as the central angle . By the Angle at the Center Theorem, we know that:
-
Applying the Theorem: According to the theorem: Substituting the given value:
-
Solving for :
Conclusion
The size of angle is .
Justification
This answer follows directly from the rule that the angle at the circumference is half of the angle at the center when both angles subtend the same arc.
Would you like further details or have any questions?
Related Questions:
- What is the Angle at the Center Theorem, and how does it apply to circles?
- How would you solve for an angle if the given central angle was different?
- Can you explain how inscribed angles relate to the diameter of a circle?
- What other properties of circles are useful in solving geometric problems?
- How can we determine the measure of an exterior angle in a circle?
Tip:
Always remember that the angle subtended by the same arc at the circumference is half the angle subtended at the center of the circle.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Circle Geometry
Angles in Circles
Formulas
Angle at the center = 2 × Angle at the circumference
Theorems
Angle at the Center Theorem
Suitable Grade Level
Grades 8-10