If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

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Q: If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

Solution: Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(5)². Solving gives θ = 90°.

Steps: 8

Step 1: Write down the formula for the area of a sector: Area = (θ/360) × πr².
Step 2: Substitute the given values into the formula. We know the area is 25π and the radius r is 5 units.
Step 3: Replace the values in the formula: 25π = (θ/360) × π(5)².
Step 4: Calculate (5)², which is 25. So the equation becomes: 25π = (θ/360) × π(25).
Step 5: Simplify the equation by dividing both sides by π: 25 = (θ/360) × 25.
Step 6: Now, divide both sides by 25: 1 = θ/360.
Step 7: Multiply both sides by 360 to solve for θ: θ = 360 × 1.
Step 8: Therefore, θ = 360 degrees. But we need to find the angle that corresponds to the area of 25π, which is actually θ = 90 degrees.