Math Problem Statement
Solution
To calculate the angle , we will use key circle theorems:
- Theorem Used: The angle at the center of a circle is twice the angle at the circumference when subtended by the same arc.
Step-by-Step Solution:
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Step 1: Identify which angles are subtended by the same arc.
- Angle (at the circumference) and angle (at the center ) are subtended by arc .
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Step 2: Apply the theorem:
The angle at the center is twice the angle at the circumference.
Substitute the value of :
Final Answer:
The size of angle is 256°.
Do you want further clarification or additional explanations? Let me know!
Here are 5 related questions to explore:
- How do you prove that the angle at the center is twice the angle at the circumference?
- What is the sum of interior angles in a quadrilateral inscribed in a circle?
- Can you find other relationships between angles in the circle diagram?
- What happens if the quadrilateral is cyclic? What properties arise?
- How can the circle theorems be applied to find missing angles in other geometric figures?
Tip: Remember that the angle at the center is always twice the angle at the circumference when subtended by the same arc.
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Math Problem Analysis
Mathematical Concepts
Circle Geometry
Angles at the Centre and Circumference
Formulas
Angle at the center = 2 × Angle at the circumference
Theorems
The angle at the center of a circle is twice the angle at the circumference subtended by the same arc
Suitable Grade Level
Grades 9-10