Math Problem Statement
Solve for x. assume the lines appear to be diameters are actual diameters
Solution
The diagram shows a circle with two intersecting diameters forming central angles. One of the central angles is labeled , and the other is labeled . Since these diameters divide the circle into two parts, the sum of the angles must equal because they form a straight line across the circle (a semicircle).
We can set up the equation:
Now, solving for :
Thus, .
Would you like further details or have any questions?
Related Questions:
- How can you verify the solution by plugging the value of back into the equation?
- What happens to the other central angle if changes?
- How would the equation change if the angle labeled was not adjacent to ?
- What if the lines were not diameters—how would the problem change?
- How does this problem demonstrate the properties of a circle’s central angles?
Tip:
Always remember that central angles formed by diameters divide the circle into equal halves, and the sum of angles along a straight line is always .
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Angles in Circles
Formulas
Sum of angles on a straight line: 180 degrees
Theorems
Central Angles Theorem
Properties of diameters in a circle
Suitable Grade Level
Grades 9-10
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