Final answer:
To find the value of x, use the formula for the area of a sector and substitute the given values. Simplify the equation to find the value of θ, which is approximately 45°.
Step-by-step explanation:
To calculate the value of x in the given question, we need to use the formula for the area of a sector:
Area of sector = (θ/360) * π * r²
Given that the radius is 14 cm and the area is 431.2 cm², we can substitute the values into the formula:
431.2 = (θ/360) * 3.1415927... * 14²
Simplifying the equation:
θ = (431.2 * 360) / (3.1415927... * 14²)
Using a calculator, we find that θ is approximately equal to 45°.