Math Problem Statement

Solve for x. assume the lines appear to be diameters are actual diameters

Solve for x. Assume the lines that 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 8585^\circ, and the other is labeled 43x143x - 1. Since these diameters divide the circle into two parts, the sum of the angles must equal 180180^\circ because they form a straight line across the circle (a semicircle).

We can set up the equation:

85+(43x1)=18085^\circ + (43x - 1)^\circ = 180^\circ

Now, solving for xx:

85+43x1=18085 + 43x - 1 = 180 84+43x=18084 + 43x = 180 43x=1808443x = 180 - 84 43x=9643x = 96 x=9643x = \frac{96}{43} x2.23x \approx 2.23

Thus, x2.23x \approx 2.23.

Would you like further details or have any questions?

Related Questions:

  1. How can you verify the solution by plugging the value of xx back into the equation?
  2. What happens to the other central angle if xx changes?
  3. How would the equation change if the angle labeled 43x143x - 1 was not adjacent to 8585^\circ?
  4. What if the lines were not diameters—how would the problem change?
  5. 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 180180^\circ.

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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